the effects of effort and intrinsic motivation on risky...

The Effects of Effort and IntrinsicMotivation on Risky Choice

Ran KivetzGraduate School of Business, Columbia University, 3022 Broadway, New York, New York 10027

[email protected]

People often need to trade off between the probability and magnitude of the rewards thatthey could earn for investing effort. The present paper proposes that the conjunction

of two simple assumptions (relating effort-induced reward expectations to prospect theory’svalue function) provides a parsimonious theory that predicts that the nature of the requiredeffort will have a systematic effect on such trade-offs. Using the case of frequency (or loyalty)programs, a series of five studies involving both real and hypothetical choices demonstratedthat (a) the presence (as opposed to absence) of effort requirements enhances the preferencefor sure-small rewards over large-uncertain rewards; (b) the preference for reward certainty isattenuated when the effort activity is intrinsically motivating; and (c) continuously increasingthe effort level leads to an inverted-U effect on the preference for sure-small over large-uncertain rewards. The studies also employ process measures and examine the mechanismsunderlying the impact of the effort stream on the trade-off between the certainty and mag-nitude of rewards. The final section discusses the theoretical implications of this researchas well as the practical implications with respect to frequency programs and other types ofincentive systems.(Effort and Reward; Decisions Under Uncertainty; Frequency/Loyalty/Reward Programs; IncentiveSystems; Intrinsic Motivation; Psychology of Rewards; Risky Choice)

“If someone tells you, ‘I have made an effort and didnot find,’ do not believe it…‘I have made an effortand did find,’ believe it.”

Babylonian Talmud (Megillah 6b)

People often need to trade off between the proba-bility and magnitude of the rewards that they couldearn for investing effort. Do we choose a job with sta-ble income or with potentially larger, albeit uncertain,compensation? Do we relegate a laborious manuscriptto become an invited book chapter (a guaranteed pub-lication) or submit it instead to a top journal (a riskybut higher-impact outlet)? Consumers, too, often faceeffort-contingent promotions and offers that differ interms of payoff and likelihood, such as when they

are enticed with rewards and (uncertain) prizes tocomplete surveys or participate in customer panels.

A fundamental question, then, is what influ-ences people’s trade-offs between the certainty andmagnitude of effort-contingent rewards. This issueis closely related to past research on decision underrisk, which has examined, for example, how peopleweigh probability versus payoff and choose amongrisky gambles (e.g., Kahneman and Tversky 1979,March and Shapira 1987, Payne et al. 1980, Sagris-tano et al. 2002, Slovic et al. 1977, Thaler and Johnson1990). Nevertheless, the impact of effort on the trade-off between the certainty and magnitude of rewardis not addressed in that research or in the volumi-nous psychological work related to effort and reward,

0732-2399/03/2204/04771526-548X electronic ISSN

Marketing Science © 2003 INFORMSVol. 22, No. 4, Fall 2003, pp. 477–502

THE EFFECTS OF EFFORT AND INTRINSIC MOTIVATION ON RISKY CHOICE

such as behaviorism (e.g., Hilgard and Bower 1975),achievement motivation (e.g., Atkinson 1957, Lewin1951), and goal setting (Locke and Latham 1990). Thepresent research proposes that the level and intrinsicinterest of effort have a predictable effect on prefer-ences toward the probability and magnitude of out-comes (e.g., choices between sure-small and large-uncertain rewards).

This proposition is tested using the case of fre-quency (or loyalty) programs. Such programs havebecome ubiquitous in the marketplace and a key com-ponent of customer relationship management, servinga critical role in developing relationships, stimulat-ing product and service usage, and retaining cus-tomers (e.g., Borenstein 1996, Deighton 2000, Drèzeand Hoch 1998, Kim et al. 2001). Frequency programs(hereafter, FPs) share a common underlying structure,whereby customers need to invest a stream of efforts(e.g., purchasing products and services, rating prod-ucts, or completing surveys) to earn future rewards.These rewards often vary in terms of their magnitudeand probability; for instance, some FPs offer a choicebetween small rewards and entries into lotteries with(uncertain) large rewards (e.g., iWon), whereas otherprograms employ one type of incentive system exclu-sively (i.e., stochastic or deterministic).

To analyze how the trade-off between the certaintyand magnitude of rewards can depend on the char-acteristics of the required effort stream, two simpleassumptions are made: (1) effort requirements cre-ate an expectation for reward (i.e., a reference pointfor evaluating the actual FP rewards), with higherrequirements leading to greater expectations; and(2) the valuation of program rewards vis-à-vis theexpectation follows the principles of prospect theory’svalue function. Combined, these two assumptionsprovide a parsimonious and unifying framework thatleads to a broad set of predictions, which have notbeen recognized before, regarding the impact of efforton risky choice. These hypotheses state that (a) thepresence (as opposed to absence) of effort require-ments enhances the preference for sure-small rewardsover large-uncertain rewards; (b) the preference forreward certainty is attenuated when the effort activ-ity is intrinsically motivating; and (c) continuouslyincreasing the effort level leads to an inverted-U effect

on the preference for sure-small over large-uncertainrewards.

The paper is organized as follows. The next sec-tion provides a theoretical analysis of the impact ofeffort on the valuation of rewards, using the twoforegoing assumptions. This analysis leads to severalhypotheses concerning the trade-off between the cer-tainty and magnitude of rewards. The hypotheses aretested in a series of five studies involving both realand hypothetical decisions, with approximately 1�800participants. The final section discusses the theoreti-cal implications of this research as well as the practi-cal implications with respect to the design of FPs andother types of incentive systems.

The Impact of Effort on theEvaluation of RewardsIn this section, the impact of effort on customer val-uation of rewards is analyzed using the context ofFPs. First, the underlying structure of such programsis discussed, and two simple assumptions are maderegarding the relationship between effort and the val-uation of rewards. This analysis leads to the pre-diction that effort requirements sensitize consumersto the presence versus absence of rewards, which istested in a preliminary study. The subsequent sectionsbuild on this analysis and examine the effect of efforton the trade-off between the certainty and magnitudeof rewards.

Frequency programs have two main components:required efforts and earned rewards. That is, earn-ing rewards typically requires consumers to investeffort (see also Soman 1998, Kivetz and Simonson2002). In many cases, such efforts are extended overtime, and rewards are contingent on reaching a cer-tain requirement level (e.g., the amount of requiredpoints or frequent-flyer miles, completed surveys orproduct ratings, or purchases before reward attain-ment). Perceived (program) effort is defined here asany inconvenience inherent in complying with theprogram requirements, such as making a special effortto buy at a particular store, purchasing more than onewould have otherwise bought, or repeatedly engagingin a certain task (e.g., completing surveys or browsingWeb sites).

478 Marketing Science/Vol. 22, No. 4, Fall 2003

KIVETZThe Effects of Effort and Intrinsic Motivation on Risky Choice

Recent research has begun exploring the relation-ship between FP efforts and rewards. For example,Kivetz and Simonson (2002) showed that consumersuse the required program effort to justify choos-ing luxury over necessity rewards. In addition, Hseeet al. (2003) demonstrated that a program’s cur-rency (e.g., points or miles) can mask an undesirableeffort-reward relationship (e.g., diminishing returnsto effort). Although this research has improved ourunderstanding of customer preference toward FPs(see also Kivetz and Simonson 2003, van Osselaeret al. 2004), the more fundamental question ofwhether and how the nature of the required earningactivity influences the trade-off between the certaintyand magnitude of rewards has not yet been studied.To explore this question, two simple assumptions aremade, as discussed next.

Effort as a Determinant of RewardExpectations: Assumption 1Requiring consumers to invest a stream of futureefforts is likely to raise expectations regarding thefair or appropriate size of the reward. Indeed, previ-ous research on equity and justice (e.g., Adams 1965,Walster et al. 1978) suggests that people expect theiroutcomes (rewards) to be proportional to their inputs(efforts). For example, equity theory’s merit princi-ple assumes that perceptions of (un)fairness are deter-mined by the balance (or lack of balance) betweenpeople’s contributions and their rewards. Moreover,equity theory proposes that both satisfaction andbehavior are linked not to objective outcomes, butrather to outcomes received relative to those judgedto be equitable.

In the context of FPs, a simple assumption (here-after, Assumption 1) is that increasing the requiredeffort level will lead consumers to expect largerrewards. Further, rewards that fail to meet the expec-tation raised by the concomitant effort level will likelybe coded as unfair losses, whereas rewards that meetor exceed the expectation level will be coded as gains.The assumption that consumers will evaluate theobjective reward relative to some psychological expec-tation level is consistent with a great deal of priorresearch on reference-dependence (e.g., Kahnemanand Tversky 1979, Thaler 1985, Winer 1986).

Next, the basic assumption that effort gives rise toexpectations is combined with the value function as aunifying framework for analyzing the impact of efforton preferences toward the certainty and magnitudeof rewards. Although other conceptualizations mayaccount for the effects of effort on reward prefer-ences, this paper demonstrates that the conjunctionof (effort-induced) reference shifts with the propertiesof the value function can account for a wide range ofpreviously unrecognized behaviors relating to riskychoice.

A Value-Function-Based Model for the Assessmentof Rewards: Assumption 2Prospect theory’s value function (Kahneman andTversky 1979; see also Thaler 1985, Tversky andKahneman 1991) incorporates three behavioral prin-ciples that are essential for the analysis of the impactof effort on reward preferences: (1) options are codedas gains and losses relative to a neutral reference out-come, which is assigned a value of zero; (2) the valuefunction is steeper for losses than for gains (i.e., lossaversion); and (3) the marginal value of both gainsand losses decreases with their magnitude (i.e., dimin-ishing sensitivity). These three characteristics lead toan asymmetric value function that is concave for gainsand convex for losses.

Although Kahneman and Tversky suggest that thereference point typically corresponds to the statusquo or current asset position, they also recognize that“there are situations in which gains and losses arecoded relative to an expectation or aspiration levelthat differs from the status quo” (Kahneman andTversky 1979, p. 286). The present paper argues thatFP effort requirements raise reward expectations thatinduce a shift in the reference away from the neu-tral status quo. Rewards are then coded as gains orlosses relative to this labile, effort-contingent referencepoint; rewards that exceed the expectation level areperceived as gains, whereas those below are perceivedas losses. Further, it is assumed that the valuation ofprogram rewards vis-à-vis the expectation follows theprinciples of prospect theory’s value function (here-after, Assumption 2).

Figure 1 illustrates this analysis. Consumers whoare not required to invest any effort to obtain a pos-sible future award, x, will perceive this award as a

Marketing Science/Vol. 22, No. 4, Fall 2003 479


Figure 1 Reference Shifts due to Required Effort

xrE

= 0 rE

>0

vE

(0)

vE

(x)

v0(x)

v0(0)

Value (no effort) Value (effort required)

GainsLosses

(free) gain with a subjective value of v0�x�.1 Theseconsumers will construe not receiving a reward as thenatural status quo and not as a loss (i.e., v0�0�= 0). Bycontrast, consumers who are required to invest effortwill expect to be compensated, and thus their rele-vant reference point will increase from zero to rE >

0. For these consumers, a lack of reward representsa loss (i.e., vE�0� � 0). This analysis gives rise to thenotion that effort requirements sensitize consumers tothe absence of rewards. That is, given Assumptions 1and 2, loss aversion and concavity of gains imply thatvE�x�−vE�0� > v0�x�−v0�0�, which means that the dif-ference in subjective value between being rewardedand not being rewarded is greater when consumersare required to invest effort. Next, before proceed-ing to the development of specific hypotheses, a pilotstudy testing the conjunction of Assumptions 1 and 2is reported.

1 This and the following analyses employ the value function v�·�from prospect theory. For example, vE�x� denotes the subjectivevalue of outcome (or reward) x, given the reference rE (i.e., effort E

is required to obtain x).

A Preliminary Test of Assumptions 1 and 2The respondents in the pilot study were 116 travelerswho were waiting for trains at sitting areas in a majortrain station. The idea was to present respondentswith either a gift (no-effort) or a FP (effort) scenarioand to ask them how happy they would be with win-ning [or not winning] a reward. Respondents wererandomly assigned to one of four conditions in a 2(effort level: gift versus FP)×2 (reward outcome: winversus not win) between-subjects design. Based on theearlier analysis and the conjunction of Assumptions 1and 2, it was predicted that the difference in hap-piness between wining and not winning the rewardwould be greater in the effort as opposed to no-effortconditions; that is, respondents would be more sensi-tive to the presence versus absence of reward whenthey were required to invest effort.

The scenarios given to the respondents in the giftconditions were:

Imagine that you receive a free gift from a car rentalcompany. The gift consists of a free entry into a lot-tery in which you could win seven free night stays atyour choice of any luxury hotel chain. The chances ofwinning are one in fifty.

You now receive your lottery entry. As it turns out,you [do not] win.

By contrast, in the FP effort conditions, respondentsreceived the following scenarios:

Imagine that you participate in a frequency programoffered by a car rental company. According to thisprogram, you are required to rent a car 10 timesbefore earning a free entry into a lottery in which youcould win seven free night stays at your choice of anyluxury hotel chain. The chances of winning are one infifty.

You now complete the required 10 car rentals andearn your lottery entry. As it turns out, you [do not]win.

Respondents were asked to rate how unhappy orhappy they would be with the outcome they wereassigned to, using an 11-point scale ranging from�−5� “Very Unhappy” to (5) “Very Happy” (the mid-point of the scale was denoted with 0 and labeled as“Neither unhappy nor happy”). The results were con-sistent with the two underlying assumptions and sup-ported the notion that effort requirements sensitizeconsumers to the difference between winning and not



winning a reward. Specifically, the difference in themean happiness rating between winning and not win-ning the reward was greater in the effort conditions(3.8 versus −18, respectively; difference = 56) than itwas in the no-effort (gift) conditions (4.1 versus −03,respectively; difference = 44), as indicated by the sig-nificant interaction between effort level and rewardoutcome �F = 44�df = 1�p < 005�. The data alsosupported the other premises underlying the pre-ceding analysis and Figure 1 (i.e., vE�0� � 0 = v0�0�;vE�x� < v0�x�).2 Next, building on the notion of effort-induced reference shifts, the impact of effort on thetrade-off between the certainty and magnitude ofrewards is considered using the case of sure-small andlarge-uncertain rewards.

The Impact of Effort on PreferencesBetween Sure-Small Rewards andLarge-Uncertain RewardsConsumer choice between sure-small rewards (e.g.,a guaranteed winning of $10) and large-uncertainrewards (e.g., a 1% chance to win $1,000) is com-mon in everyday life and, increasingly, in marketingpromotions and programs. Accordingly, such choiceshave received a great deal of attention from con-sumer and decision researchers (see, e.g., Kahnemanand Tversky 1979, 1981; Thaler and Johnson 1990).Normative theory indicates that decisions under riskshould be influenced by consumers’ risk preferences,as determined by the shape (concavity) of their utilityfunctions (Arrow 1971). However, previous researchhas revealed a number of behavioral factors that

2 Specifically, respondents assigned to the loss condition were sig-nificantly more unhappy when the (unattained) reward was con-tingent on complying with a FP effort stream than when it was agift (M = −18 versus M = −03, t = 39; p < 0001; medians = −20versus 0). Moreover, while the average happiness rating of respon-dents in the effort-loss condition was significantly lower than thezero midpoint of the scale �t = 54�p < 0001�, the average happi-ness rating of respondents in the gift-loss condition was not �t =15�p > 01�. In addition, respondents assigned to the gain conditionwere directionally happier when the reward was a gift than when itwas contingent on complying with effort (M = 41 versus M = 38,t = 06; p > 01; both significantly greater than zero; medians = 50versus 4.0).

influence such decisions, including the framing of thedecision problem (Kahneman and Tversky 1979, 1981)and prior outcomes (Laughhunn and Payne 1984,Thaler and Johnson 1990). In this article, it is arguedthat an important yet unrecognized determinant ofrisky choice is the level and intrinsic interest of therequired effort.

Specifically, building on the earlier analysis thateffort sensitizes consumers to the presence (versusabsence) of rewards, it is posited that the introduc-tion of effort requirements will enhance the pref-erence for sure-small rewards over larger-uncertainrewards. That is, as long as the sure-small reward isperceived as sufficient compensation for the requiredeffort, ensuring that one does not work for nothingwill serve as a compelling reason for choosing thesure-small reward. By contrast, selecting the large-uncertain reward leaves open the possibility of exert-ing effort in return for no reward, an outcome that iscoded as a loss relative to the effort-induced rewardexpectation.

The notion that the presence (as opposed to absence)of effort requirements will shift consumer choice infavor of the certain reward can be predicted using theconjunction of the two assumptions discussed earlier(i.e., (1) effort creates an expectation or reference point,and (2) the valuation of FP rewards relative to thereward expectation is consistent with the value func-tion). To illustrate this argument, consider outcomes sand l shown in Figure 2, where l > s, but the probabil-ity of obtaining outcome l is considerably smaller thanthe certainty of attaining outcome s (i.e., pl � ps = 1).When no effort is required to obtain a choice betweenthe sure-small and large-uncertain rewards, the differ-ence in subjective value between these two rewards isequal to v0�s�− �pl ∗v0�l�+�1−pl�∗v0�0��.3 Conversely,when earning a choice between these rewards is con-tingent on effort, the shift in the reference point (dueto a positive reward expectation) will result in a dif-ferent relative reward valuation, vE�s�− �pl ∗ vE�l�+�1−pl�∗vE�0��.

3 This and the subsequent analyses assume that consumers adoptthe explicit probabilities (i.e., p) stated for the various rewards.Replacing these probabilities with prospect theory’s decisionweights (i.e., ��p�) does not alter the nature or conclusions of theanalyses.



Figure 2 The Impact of Effort-Induced Reference Shifts on ChoicesBetween Sure-Small and Large-Uncertain Rewards

s lrE

= 0 rE

> 0

vE(0)

vE(s)

vE(l)

v0(l)

v0(s)

v0(0)

Value (no effort) Value (effort required)

GainsLosses

This shift in reference from zero to rE > 0 leads totwo opposing effects regarding the relative value ofthe sure-small and large-uncertain rewards. On onehand, loss aversion means that the possibility �1−pl�

of not being rewarded for investing efforts (inherentin the large-uncertain reward) will enhance the rela-tive preference for the sure-small reward, which guar-antees winning (note that vE�0� < v0�0� = 0). On theother hand, the concavity of the gain function impliesthat the perceived difference between l and s willbe greater under the new reference point rE > 0 (i.e.,vE�l�−vE�s� > v0�l�−v0�s�).

The relative strength of these two opposing effectswill be determined by the probability of winning l;the lower pl is, the greater the impact of theloss-aversion effect relative to the concavity effect.Appendix A (Proposition 1) shows that under ahighly plausible condition, namely a coefficient of lossaversion of at least two (e.g., Tversky and Kahneman1991), the loss aversion effect always outweighs theconcavity effect if the probability of winning l is

smaller than 0.5. Thus, as long as pl < 05 and thesure-small reward meets or exceeds the expectationfor reward raised by the effort requirement (i.e.,s ≥ rE), the introduction of effort will enhance the rel-ative preference for the sure-small reward over thelarge-uncertain reward. This conveys the intuitionthat, compared to a no-effort condition, consumerswho are required to invest efforts will prefer a surecompensation �s� over a potentially larger reward �l�

that is more likely to end up as a perceived loss (i.e.,because �1−pl� = p0 > 05 and vE�0� < 0).

The discussion leads to the following hypothesis:4

Hypothesis 1. Consumers are more likely to prefersure-small rewards over large-uncertain rewards when theyare rewarded for the expenditure of effort compared to whenthey are provided with effort-free rewards.

This prediction, of course, does not mean thathigher effort will always enhance the relative shareof the sure-small reward, considering that greatereffort requirements can lead at some point to expec-tations that are not met by the sure-small reward.Thus, the condition that the sure-small reward satis-fies consumers’ expectations is later relaxed by exam-ining the effects of an extended range of increasesin the required effort. These investigations reveal asystematic and conceptually rich association betweenrequired effort and risky choice. Next, a studydesigned to test Hypothesis 1 is discussed.

Study 1: Choices BetweenSure-Small and Large-UncertainRewards as a Function of EffortMethodParticipants. The participants in the study were

436 travelers who were waiting for trains at sittingareas in a major train station. They were between 18and 70 years old and represented a wide range ofdemographic characteristics.

4 This hypothesis, as well as Hypotheses 2 and 3 discussed subse-quently, assume that the conditions delineated above are satisfied(i.e., pl < 05 and s ≥ rE).



Figure 3 Test of Hypothesis 1—Frequent Cereal-Eater Scenario

Effort Condition:

Frequent-Cereal Eater Program

Imagine that a national brand of cereals offers you the opportunity to participate in a “frequent-cereal eater” program. According to

this program, after you purchase ten boxes of this brand of cereal, you will earn a choice between the two rewards below:

Circle the reward that you prefer to receive if you complete ten purchases of cereal boxes:

A B

No-Effort Condition:

Frequent-Cereal Eater Program

Imagine that a national brand of cereals offers a friend of yours the opportunity to participate in a “frequent-cereal eater” program.

According to this program, after your friend purchases ten boxes of this brand of cereal, s/he will earn a choice between the two rewards

below. However, your friend is not interested in airline miles, and therefore, tells you that if s/he earns the reward, s/he will give it to you:

Circle the reward that you prefer to receive from your friend if s/he completes ten purchases of cereal boxes:

A B

Reward A

1000 frequent-flyer miles

(accepted by any frequent-flyer program)

Reward B

One in fifty chance to win 50,000 frequent-flyer miles


Reward A

1000 frequent-flyer miles


Reward B

One in fifty chance to win 50,000 frequent-flyer miles


Procedure and Design. Hypothesis 1 was testedin three scenarios involving a frequent cereal-eaterprogram (98 respondents), a grocery store problem(152 respondents), and a hotel problem (186 respon-dents).5 In each scenario, respondents were ran-domly assigned to one of two (between-subjects)conditions, either an (FP) effort condition or a no-effort condition. Specifically, in the frequent cereal-eater program (see Figure 3), effort was manipulatedby informing respondents that they would receive

5 Although the scenarios were run separately, all three appear underStudy 1 because they employed a similar methodology. Of the 131participants in the frequent-cereal eater program, 33 respondentswere not included in the analysis (leaving 98 respondents) becausethese respondents indicated that they did not participate in anyfrequent-flyer program, and therefore the rewards (frequent-flyermiles) were irrelevant to them.

a choice between two rewards after either they ortheir friend purchased 10 cereal boxes (i.e., pres-ence vs. absence of personal effort, respectively).In the grocery store problem (see Appendix B),respondents received a choice between two rewards,either after they completed five grocery purchasesor as an appreciation gift. And, in the hotel prob-lem (see Appendix B), respondents could obtain achoice between rewards by participating in either anFP (that required 10-night stays) or an (effortless) freeraffle. As shown in Figure 3 and Appendix B, thethree problems had a similar format, with respon-dents choosing between a sure-small reward and alarge-uncertain reward.6 In the hotel scenario, respon-dents also had the option of not participating in the

6 In the frequent cereal-eater program and in the hotel problem,the expected values of the sure-small and large-uncertain rewards



FP (or raffle) (see Dhar and Simonson 2003). As acheck for the effort manipulation, after making theirchoices respondents in all three problems rated thedegree to which attaining the reward involved effortfor them, using an 11-point scale ranging from (0) “Noeffort at all” to (10) “Very high effort.”

Results

Manipulation Checks. In all three problems, themanipulation of effort produced the expected effortperceptions, with respondents in the FP effort con-dition indicating higher mean perceived effort com-pared to respondents in the no-effort condition(X = 38 versus X = 14 in the frequent cereal-eaterprogram, and X = 53 versus X = 28 in the hotel prob-lem, both ps< 005; X = 34 versus X = 26 in the gro-cery store problem, p = 006).

Reward Choices. The results of all three problemssupported Hypothesis 1. More specifically, in the fre-quent cereal-eater program, the choice share of thesure-small reward was higher in the effort condi-tion than in the no-effort condition (77% (36 out of47 respondents) versus 61% (31 out of 51 respon-dents); t = 17; p < 005). Similarly, in the grocery storeproblem respondents were significantly more likely tochoose the sure-small reward in the effort conditionthan in the no-effort condition (73% (60/82) versus49% (34/70); t = 32; p < 0001). Finally, in the hotelproblem, the introduction of effort led to a significantincrease in the relative share of the sure-small rewardfrom 46% (i.e., 46 out of 99 respondents who chose areward) in the no-effort condition to 74% (i.e., 51 outof 69 respondents who chose a reward) in the effortcondition �t = 38�p < 0001�.

DiscussionThe results provide support for the role of effortin determining risky choice, indicating that whenrewards are contingent on complying with an effortstream, consumers’ preferences shift in favor ofsure-small rewards at the expense of large-uncertain

were equal. In the grocery store problem, the expected value ofthe large-uncertain reward was greater than that of the sure-smallreward.

rewards. It is important to note that these resultswere obtained regardless of whether or not a no-choice option was available. Next, two studies arepresented that address more directly the mechanismsunderlying the impact of effort on the trade-offbetween the certainty and magnitude of rewards. Inparticular, these studies investigate whether the pref-erence for sure-small rewards over large-uncertainrewards is greater among consumers with lowerintrinsic motivation to engage in the required effortactivity. A second way in which the theoretical expla-nation is tested is by manipulating (rather than mea-suring) the intrinsic interest of an effort activity andexamining the impact of effort (relative to a no-effortcondition) on the preferred reward.

The Role of Intrinsic MotivationThe impact of effort on preference for sure-smallrewards was predicted based on the notion that effortrequirements give rise to reward expectations, andtherefore to a feeling of loss when no reward isafforded. However, people who see themselves asintrinsically motivated to engage in an effort activityare less likely to make the attribution that they areengaging in the activity only to obtain some extrinsicincentive and are rather more likely to attribute theirparticipation to the enjoyment, satisfaction, and/orinterest inherent in the effort activity (see, e.g., Deciand Ryan 1985, Lepper 1981, Lepper and Greene1978). Further, because the expectation for (extrinsic)reward is likely to be lower for intrinsically moti-vated individuals, it is predicted that the preferencefor sure-small rewards will be weaker among suchindividuals. Thus:

Hypothesis 2. Relative to individuals with highintrinsic motivation to engage in an effort activity, individ-uals with low intrinsic motivation are more likely to prefersure-small rewards over large-uncertain rewards.

Relatedly, when an effort activity is inherentlyenjoyable (i.e., intrinsically motivating), it is likelyto lead to lower reward expectations and, therefore,have a weaker effect on FP reward preferences. Forinstance, a program that requires consumers to reviewproducts (e.g., Epinions.com) is less likely to raise an



expectation of reward if consuming (and reviewing)the relevant products is enjoyable. Accordingly, it ispredicted that the introduction of an effort require-ment will have a stronger positive effect on the rel-ative share of the sure-small reward when the effortactivity is not intrinsically motivating. This leads tothe following interaction hypothesis:

Hypothesis 3. The positive impact of effort (comparedto an effort-free condition) on the preference for sure-smallover large-uncertain rewards is stronger for effort activitiesthat are not intrinsically motivating.

Hypotheses 2 and 3 were examined in the followingtwo studies. The first study tests the role of intrin-sic motivation in determining reward preferences bymeasuring participants’ pre-existing interests in therequired effort activity.

Study 2: Intrinsic Motivation as aDeterminant of Reward PreferencesHypothesis 2 was tested by measuring participants’intrinsic motivation to engage in an effort activity.Moreover, to allow for a strong test of the role ofintrinsic motivation, the participants in this studymade real choices. In addition, to further explorethe mechanisms underlying the impact of effort onreward preferences, the choice explanations providedby these participants are subsequently examined.

Method

Participants. The participants were 232 students atan East Coast high school. Participants were recruitedby schoolteachers at the beginning of a regular class-room session. As explained later, the participantswere randomly assigned to conditions.

Procedure and Design. At the beginning of a reg-ular classroom session, several of the high schoolteachers informed their classes that the school wasconsidering introducing some new learning materi-als. Therefore, these students have been selected toparticipate in a four-week study during which theywill have to use and evaluate these learning mate-rials. The teachers then distributed to their students

a (supposedly) official survey from the high school.Students were randomly assigned to one of twopossible versions of the survey, regarding either anew math curriculum or a new poetry curriculum.In both survey conditions, students were informedthat they would be asked to solve three math prob-lems [read and critically analyze three poems] perweek for four consecutive weeks. Further, once aweek, after solving the math problems [reading andanalyzing the poems], they would need to completea survey evaluating the math workbook [poetry col-lection]. In order to familiarize students with theirfuture task, both survey versions asked students toreview a set of sample math problems [poems] andevaluation questions, which were printed on a sepa-rate sheet of blue card-stock paper. The sample mathproblems were taken from the January 2001 Mandel-brot Competition Greater Testing Concepts companyand from the Round 4, Academic Year 2000–2001 USAMathematical Talent Search. The sample poems weretaken from the Real SAT II: Subject Tests (CollegeBoard 1998).

Students in both conditions were informed thatcompletion of the required effort would earn one oftwo rewards, either $20 in cash (a sure-small reward)or a 1 in 25 chance to win $600 in cash (a large-uncertain reward). Students were asked to indicatein advance which reward they choose to earn uponcompletion of the required effort, so that the schoolcould plan ahead. After they chose a reward, studentswere asked to return their survey to the teacher. Stu-dents were then given an additional page on whichthey were asked to rate how much they like mathand poetry. The ratings were on a seven-point scaleranging from “I like math [poetry] much less than typ-ical students” (1) to “I like math [poetry] much morethan typical students” (7). These math/poetry-likingratings served as a measure of participants’ intrinsicmotivation to engage in the effort activity. In addi-tion, students were asked to indicate how many timesthey solved a math problem [read a poem] in a typi-cal month. Students were also asked to explain theirchoice of reward in writing. Students next listed, infree response, any other thoughts they had about thecurriculum survey. None of the participants expressedsuspicion about the survey’s purpose or articulatedthe actual hypotheses being tested.



ResultsParticipants assigned to the math task were dividedinto two groups, “math haters” and “math lovers,”based on a median split of their reported liking ofmath (means and standard deviations of math-likingratings in the “math haters” versus “math lovers”groups were 2.8 �sd = 11� versus 5.7 �sd = 07�,respectively). Similarly, participants assigned to thepoetry task were divided into two groups, “poetryhaters” and “poetry lovers,” based on a mediansplit of their reported liking of poetry (means andstandard deviations of poetry liking ratings in the“poetry haters” versus “poetry lovers” groups were2.7 �sd = 11� versus 5.9 �sd = 08�, respectively).

Participants’ reward choices were then examinedto test H2, which predicts that math [poetry] haterswill be more likely to choose the sure-small rewardcompared to math [poetry] lovers. Consistent withthe intrinsic motivation hypothesis, the choice shareof the sure-small reward was higher among “mathhaters” than among “math lovers” (79% versus 64%;t = 18; p < 005). Similarly, the share of the sure-small reward was higher among “poetry haters” thanamong “poetry lovers” (84% versus 70%; t = 18;p < 005).

In addition, students were asked to indicatewhether they participated in the school’s math team(a math club involving yearlong national competi-tions in math). Consistent with the notion that indi-viduals are less likely to expect an extrinsic rewardfor engaging in an activity that they view as intrinsi-cally interesting, in the math condition, students whowere members of the math team were less likely tochoose the sure-small reward compared to studentswho were not members of the math team (56% versus74%; t = 16; p < 006). This result cannot be explainedas reflecting a greater tendency of math team mem-bers to calculate the expected value of the rewards(which was lower for the sure-small reward) because,in the poetry condition, math team members were notless likely to prefer the sure-small reward comparedto nonmembers (84% versus 76%; t = 09; p > 01).

In summary, this study demonstrated the impactof intrinsic motivation using an unobtrusive mea-sure of task liking, in the context of an actualrewards program with real potential consequences.

Consistent with the notion that intrinsically motivatedindividuals are less likely to expect a reward, theresults indicate that the preference for the sure-smallreward is significantly weaker among such partici-pants. Next, a study is reported that further examinesthe role of intrinsic motivation and tests Hypothesis3, which predicts that enjoyable effort has a weakereffect on preferences for sure-small rewards.

Study 3: Intrinsic Motivation asa Moderator of the Impact of Efforton Preferred RewardsHypothesis 3 was tested by manipulating the enjoy-ment inherent in an effort task (reading and reviewingmagazines) and examining the interaction betweenintrinsic motivation and the level of effort withrespect to preferences between sure-small and large-uncertain rewards. To vary the level of task enjoy-ment, a pretest was conducted in which respondents(148 travelers waiting for trains) were asked whichweekly magazines they read most often and whichmagazine topic most interests them. On the basis ofthe pretest results, two magazines were chosen oflow versus high intrinsic interest for the respondentpopulation (i.e., Better Homes & Gardens versus Time,respectively).

MethodThe participants in the study were 311 travelers whowere waiting for trains at sitting areas in a majortrain station. Participants were randomly assignedto one of four conditions in a 2 (effort level: noeffort versus FP effort) × 2 (interest level: low ver-sus high) between-subjects design. Respondents werefirst asked to familiarize themselves with the mag-azine they were assigned to, either Better Homes &Gardens (low intrinsic interest) or Time (high intrinsicinterest). They received a description and photographof the magazine, adopted with minor adjustmentsfrom MagazineOutlet.com and Epinions.com. Afterreading about the magazine, respondents consideredeither a free promotion or a frequency program, bothoffered by the magazine they read about earlier. Inthe free promotion (no-effort) condition, respondents



were told that in an attempt to increase awareness ofthe magazine, the publishers are sending them fourfree issues as well as a free gift, which consistedof a choice between two rewards. In the FP effortcondition, respondents were told that in an attemptto improve the magazine’s content and design, thepublishers are offering them the option of earninga reward in return for reading and providing feed-back on four (free) issues of the magazine (oncea week, after reading the magazine, they wouldneed to complete a three-minute phone survey). Inboth conditions, respondents were asked to choosebetween two alternative rewards, either two freemovie tickets (a sure-small reward) or a free entryinto a lottery with a 1 in 100 chance to win a vaca-tion package for two in Hawaii (a large-uncertainreward). Respondents were also given the option ofnot participating.

As a check for the manipulation of intrinsic interest,a subsample of respondents rated (after making theirchoice) the extent to which they enjoyed (or wouldenjoy) reading the two magazines on an 11-pointscale ranging from “I would not enjoy it at all” (0)to “I would enjoy it greatly” (10). These respondentsalso indicated how many times they read each mag-azine in a typical month. As expected, reading Timewas rated as significantly more enjoyable than read-ing Better Homes & Gardens (M = 60 versus M = 40,t = 42; p < 0001); further, the average enjoyment rat-ing for Time was significantly higher than the scalemidpoint of five �t = 24�p < 005�, whereas the aver-age rating for Better Homes & Gardens was signifi-cantly lower �t = 24�p < 005�. The enjoyment ratingswere also significantly correlated with the frequencyof reading the magazines (r = 05 and r = 06 forTime and Better Homes & Gardens, respectively; bothps < 0001). Combined, these checks confirm that themanipulation of magazine type affected respondents’intrinsic motivation in the expected direction.

ResultsConsistent with Study 1 and Hypothesis 1, in bothmagazine versions, the relative choice share of thesure-small reward was higher in the FP effort con-dition than in the no-effort (gift) condition. Pooled

across the level of intrinsic motivation, there wasa significant main effect of effort level on thepreference for the sure-small reward (60% versus 43%;t = 29; p < 0005). More importantly, consistent withHypothesis 3, whereas the effect of effort in the BetterHomes & Gardens condition (low intrinsic motivation)was statistically significant, the effect in the group thatconsidered Time magazine (high intrinsic motivation)was weaker and not statistically significant.

Specifically, in the low intrinsic motivation condi-tion, when the reward was not contingent on effort(i.e., it was a gift), 38% (27 out of 71) of respondentschose the sure-small reward over the large-uncertainreward. However, when earning the reward requiredinvesting effort, 66% (41 out of 62) preferred the sure-small reward, an increase of 28% �t = 34�p < 0001�.By contrast, in the high intrinsic motivation condi-tion, when the reward was a gift, 48% (35 out of 73)of respondents chose the sure-small reward over thelarge-uncertain reward. However, when the rewardrequired investing efforts, the relative share of thecertain reward was 55% (41 out of 74), an increaseof only 7% �t = 09�p > 01�. The difference betweenthe two intrinsic motivation conditions in the impactof effort on reward choice was statistically signifi-cant (28% versus 7%; t = 18; p < 005). In addition,respondents assigned to the FP effort conditions weremore likely to choose the sure-small reward whenthe effort activity was not intrinsically motivating(reading and reviewing Better Homes & Gardens) thanwhen the effort activity was intrinsically motivating(reading and reviewing Time). This effect, which wasmarginally significant (66% versus 55%; t = 13; p <

01), is consistent with Hypothesis 2 and the resultsof Study 2.

The Role of Intrinsic Motivation: DiscussionUsing two methodologies, it was demonstrated thatthe preference between sure-small and large-uncertainrewards depends on the intrinsic motivation toengage in the required effort activity. Consistent withthe notion that intrinsically motivating effort is lesslikely to lead to an expectation of extrinsic reward,it was shown that individuals who liked a particu-lar effort activity (e.g., solving and reviewing math



problems) were less likely to prefer the sure-smallreward compared to individuals who disliked thisactivity. While this demonstration was based on ameasurement of participants’ pre-existing tastes, asecond study involved a manipulation of the inter-est inherent in the effort task (using low versus high-enjoyment magazines). As suggested by the notionthat engaging in intrinsically motivating (or reward-ing) effort lowers the expectation for extrinsic rein-forcement, the findings indicate that the positiveimpact of an effort requirement (compared to a no-effort condition) on the preference for reward cer-tainty was attenuated when the effort was enjoyable.

To further examine the proposed account for effort-contingent reward preferences and the role of intrin-sic motivation, the choice explanations from Study 2were analyzed; these explanations were provided bythe 232 high school students who made a real choicebetween $20 in cash (a sure-small reward) and a 1in 25 chance to win $600 in cash (a large-uncertainreward). Two independent judges who were unawareof the study’s predictions coded the choice explana-tions; the interjudge reliability was 92%, and disagree-ments were resolved by discussion. Given that theresults pertaining to the poetry and math tasks weresimilar, the analysis is pooled across these two condi-tions. This analysis contrasts the reasons provided byparticipants with low versus high intrinsic motivationto engage in the required effort activity.

Among participants with low intrinsic interest inthe effort task (math and poetry “haters”) who chosethe sure-small reward (94/115), 31% explained theirchoice based on the notion that they expect a guaran-teed reward in return for investing (dislikable) efforts.By contrast, among participants with high interestin the effort activity (math and poetry “lovers”)who chose the sure-small reward (78/117), only 4%used this explanation. The following are examplesof explanations for choosing the sure-small rewardthat were coded as reflecting effort-contingent rewardpreferences:

• “I would want to be guaranteed the moneybecause I don’t like poetry that much.”

• “$20 is guaranteed. $600 is nice, but big chance ofgetting NOTHING in return. That would be horrible.”

• “I’m lazy as hell about math. I only do thingsthat I like, such as reading, acting, or critiquing films.So I want a definite reward.”The finding that participants were more likely toexplain choosing the sure-small reward based onthe required effort when they disliked rather thanliked the effort activity supports the notion of effort-contingent reward preferences and the moderatingrole of intrinsic motivation.

In addition, analysis of the reasons provided byintrinsically motivated participants who chose thelarge-uncertain reward indicated that 33% explainedtheir choice based on the notion that the (likable)effort activity is rewarding in itself, and thereforea lack of extrinsic reinforcement would not constitutea loss or disappointment. Conversely, none of the par-ticipants with low intrinsic motivation who chose theuncertain reward used this explanation. Examples ofsuch reasons include:

• “I like math so it would be okay if I didn’t winanything and why not have the chance to win $600.”

• “At first I thought $20, but changed my mind—$20 isn’t that much money and I’d be reading poetryanyway, so I don’t feel like I’d HAVE to be compen-sated for it.”

• “To me, math is pretty much nothing—in fact, Ilike doing math. So getting paid for doing somethingI like to do is a bonus.”

Interestingly, however, among participants whochose the uncertain reward, those with lower intrinsicmotivation were much more likely (43% versus 3%)to explain their choice as an attempt to “break even”(Thaler and Johnson 1990). That is, these participantsindicated that the sure-small reward was insufficientas a compensation for the (dislikable) effort involved,using reasons like: “Twenty dollars is not enough tocompensate for reading poetry for four weeks. Six-hundred dollars is”; “$20 is not significant enough forthe amount of work involved. Maybe if the rewardwas $50+ I would take it, but I would rather takea chance (1/25 isn’t too bad) at the big cash prize.”Accordingly, the next section examines the effect of asystematic manipulation of required efforts, wherebybeyond a certain effort level, the impact of effort onpreferences between sure-small and large-uncertainrewards reverses.



The Curvilinear RelationshipBetween Effort and Preference forSure-Small Over Large-UncertainRewardsSo far, we have focused on situations in which mostconsumers perceived the sure-small reward as suf-ficiently large relative to the effort-induced rewardexpectation and examined the impact of the presenceversus absence of effort on reward preferences. Here,it is suggested that, as long as the sure-small reward issatisfactory, further increasing the required efforts andthe concomitant reward expectations will enhance theaversion and perceived loss related to the potentialabsence of reward (inherent in the large-uncertainreward). Thus, because the sure-small reward elim-inates the possibility of such a (perceived) loss, the

Figure 4 The Curvilinear Relationship Between Effort and Preference for Sure-Small over Large-Uncertain Rewards

Reward Expectations Not Satisfied by Sure-Small Reward

s = rE3 lrE = 0v0(0) = 0

rE4

Value(no effort)

vE3(0)

vE3(l)

vE3(s)

Value(effort E4)

Value(effort E3)

vE4(0)

vE4(s)

vE4(l)

rE5

vE5(l)

vE5(s)

vE5(0)

Value(effort E5)

Reward Expectations Satisfied by Sure-Small Reward

s l

v0(l)

v0(s)

rE = 0v0(0) = 0

rE1

vE1(l)

vE1(s)

vE1(0)

Value(no effort)

vE2(0)

vE2(l)

vE2(s)

Value(effort E1)

Value(effort E2)

rE2

preference for this reward is predicted to increasewith greater effort.

This intuition is illustrated in the left-hand sideof Figure 4, which depicts incremental effort-inducedreference shifts that do not exceed the magnitude ofthe sure-small reward (i.e., s > rE2 > rE1 > 0). As dis-cussed earlier, under this condition, increasing thereference point leads to two opposing forces regard-ing the relative value of the sure-small and large-uncertain rewards. The concavity of the gain functionimplies an increasing difference between the per-ceived values of l and s. However, as long as theprobability of obtaining the large-uncertain reward isreasonably low (i.e., pl < 05), this effect will be out-weighed by the impact of loss aversion. That is, asthe reference point increases, the considerable pos-sibility �1 − pl� of not being rewarded for investing



efforts becomes more aversive and looms larger thanthe enhanced sensitivity to the size of rewards (seeAppendix A, Proposition 2 for a formal proof).7

However, reward expectations that exceed themagnitude of the sure-small reward give rise toa diametrically opposed effect. Specifically, in suchcases, the sure-small reward is perceived as a sureloss, whereas the large-uncertain reward provides thepossibility (albeit low) of avoiding such a loss andreceiving adequate compensation. Thus, to escapewhat they perceive as a certain loss, consumersmay switch to the large-uncertain reward when theirreward expectations surpass the sure-small reward. Insuch situations, further increasing the effort require-ments is predicted to enhance the preference for thelarge-uncertain reward because the rising expecta-tions increase the perceived loss associated with theunsatisfactory small reward. The notion that con-sumers will prefer the large-uncertain reward whenthe sure-small reward does not meet their expecta-tions is supported by the findings of risk seeking inthe domain of losses (e.g., Kahneman and Tversky1979, Payne et al. 1980) and break-even effects (Thalerand Johnson 1990), whereby consumers tolerate morerisk when they are offered the opportunity to elimi-nate prior losses.

This conceptualization is depicted in the right-handside of Figure 4, in which the effort-based referenceshifts occur to the right of the sure-small reward (i.e.,s = rE3 < rE4 < rE5). In this case, increasing the referencepoint leads to two consistent effects, namely loss aver-sion and diminishing sensitivity of the gain and lossfunctions; both of these effects enhance the value ofthe large-uncertain reward relative to the sure-smallreward.

The discussion leads to the following hypothesis:

Hypothesis 4. The preference for sure-small rewardsover large-uncertain rewards is an inverses U-function ofthe required effort level.

7 As shown in Appendix A (Proposition 2), because the gain func-tion may become very steep close to the reference point, the rangeof reference shifts (increases) in which this effect will occur mayhave an upper bound of s/2 as opposed to s. The essence of theargument made in this section holds even with this lower limit.

This prediction, of course, does not mean that oncethe expectation exceeds the sure-small reward, highereffort will always enhance the relative share of thelarger reward, considering that greater effort require-ments can lead at some point to heightened expec-tations that overshadow even the larger reward (seeAppendix A, Proposition 2) and can eliminate partic-ipation in the program (see also Dhar 1997, Dhar andSimonson 2003). Next, two studies are described thatwere designed to test Hypothesis 4 by systematicallyincreasing the level of required effort and elicitingreward choices with real consequences.

Study 4: The Curvilinear Effect ofEffort on Reward Preferences—TheOnline Music ProgramMethodThe participants in the study were 161 students at alarge East Coast university, recruited outside of themain university library. Participants were informedthat a group of MBA students were launching a newonline (Internet) music site that would reward usersfor reviewing and rating songs and would providefree news and information about concerts and othermusic events. Participants were asked to complete aquestionnaire that was described as part of an effortto determine the best rewards for the music Web site.

Participants were randomly assigned to one of fourconditions. Three (effort) conditions involved review-ing and rating (5, 30, or 70) songs over the Internet.In these three conditions, completion of the requiredeffort would earn a choice between two rewards,either a free music CD of the participant’s choice(a sure-small reward) or a free entry into a lotterywith a 1 in 30 chance to win a portable MP3-CDplayer (a large-uncertain reward). The fourth condi-tion did not involve any effort, but rather a choicebetween two (effort-free) rewards (described above)that were part of a free promotion. In all four condi-tions, respondents were also given the option of notchoosing either reward and not participating in the FPor promotion (in each of the four conditions, no morethan one respondent chose this option). The informa-tion provided to participants about the music Web sitewas held constant across the four conditions.



Table 1 Perceived-Effort Ratings in the Online Music Program

95% Confidence IntervalNo. of Required Mean Perceived- Std.Song Ratings Effort Rating Error Lower Bound Upper Bound

0 3�3 0�34 2�7 4�05 4�3 0�36 3�6 5�030 5�6 0�32 5�0 6�270 6�4 0�32 5�8 7�1

Note. Dependent variable: Perceived-effort rating (0–10).

After making their choice, participants were givenan additional page on which they rated the degree towhich attaining the reward involved effort for them,using an 11-point scale ranging from (0) “No effort atall” to (10) “Very high effort.” These ratings served asa check for the effort manipulation.

ResultsParticipants’ effort ratings confirmed that the manip-ulation affected perceived effort in the expecteddirection. Specifically, the mean perceived-effort rat-ing strictly increased with the number of requiredsong ratings, with each requirement conditionperceived as significantly more effortful than theadjacent lower-effort condition (see Table 1).

A logistic regression was used to test Hypothesis4, which predicts that the preference for the sure-small reward over the large-uncertain reward willbe an inverse U-function of the required effort level.The (dummy) dependent variable received a valueof 1 [0] if the sure-small [large-uncertain] rewardwas chosen. The independent variables includedthe effort requirement level (0, 5, 30, or 70 songratings) and a (mean-centered) quadratic effort term.As predicted by Hypothesis 4, the quadratic termwas statistically significant and in the hypothesizeddirection �wald-�2 = 52; p < 005�, indicating a signif-icant curvilinear effect of effort.8 Specifically, in theno-effort condition, the relative choice share of thesure-small reward was 60% (24 out of 40 participants),whereas in the 5-, 30-, and 70-song ratings (effort)conditions, the relative share of this reward increasedto 88% (29/33), but then decreased to 84% (36/43) and65% (28/43), respectively (see Figure 5).

8 Wald-�2 is the statistical test used in logistic regressions through-out the article.

Figure 5 The Curvilinear Effect of Effort Requirements on Preferencefor Sure-Small over Large-Uncertain Rewards—The OnlineMusic Program

60%

65%

88%

84%

40%

50%

60%

70%

80%

90%

100%

0 5 30 70

Number of Required Song Ratings

Sh

are

of

Su

re-S

mal

lR

ewar

dTo further examine the relationship between the

construct of effort and reward preferences, a logis-tic regression was used in which the independentvariables were the 11-point perceived-effort ratingsand a (mean-centered) quadratic perceived-effortterm. Consistent with Hypothesis 4, the quadraticperceived-effort term was statistically significantand in the hypothesized direction �wald-�2 = 41;p < 005�, indicating that the share of the sure-smallreward was an inverse U-function of the perceived-effort ratings.

Study 5: The Curvilinear Effect ofEffort on Reward Preferences—TheOnline Survey ProgramThe results of the previous study supported thehypothesis that effort has a curvilinear effect onthe preference for sure-small over large-uncertainrewards. However, only a limited number of effortlevels were used. Accordingly, the present study wasdesigned to allow for a stronger test of the inverse-Uhypothesis by employing a greater number of effortlevels (i.e., seven). In addition, a process measurewas used to investigate more directly the notionthat higher effort requirements increase consumers’reward expectations.

The current study was also used to examine theeffect of a systematic manipulation of whether the



rewards are the primary or secondary motivationfor engaging in the effort activity. Specifically, whenconsumers are directly compensated (e.g., with sub-stantial monetary payments) for their efforts, theexpectation of additional extrinsic reward is likely tobe attenuated. In such cases, consumers are predictedto be less averse to the possibility of not receiving anFP reward.

MethodThe participants in the study were 465 travelers whowere waiting for trains at sitting areas in a majortrain station. Participants were informed that thebusiness school (of a large East Coast university) wasimplementing a program in which people completeshort surveys online in return for rewards. Partici-pants were asked to complete a questionnaire thatwas described as part of an effort to determine thebest reward for the program.

Participants were randomly assigned to one ofseven conditions. Five (effort) conditions involvedcompleting (3, 5, 8, 10, or 15) surveys over the Internet(each survey was described as taking about five min-utes to answer). In these five conditions, completionof the required effort would earn a choice betweentwo rewards, either two movie tickets (a sure-smallreward) or an entry into a lottery with a 1 in 30 chanceto win 80 movie tickets (a large-uncertain reward).A sixth condition did not involve any effort, butrather a choice between the two rewards as part ofa free promotion. A seventh condition was designedto test the prediction that reward expectations areattenuated when consumers have another primarymotivation for engaging in the required efforts. Thiscondition was identical to the five-survey conditionmentioned earlier, except that completing each sur-vey earned $50 (a total of $250 for five surveys).Completion of the five surveys also earned a choicebetween the two rewards discussed above. It wasexpected that the preference for the sure-small rewardwould be stronger when no ($50) monetary compen-sation was given on a per-survey basis. In all sevenconditions, respondents were also given the optionof not choosing a reward. The information providedabout the program was held constant across the sevenconditions.

After making their choice, participants were askedto indicate whether or not each of the two rewardswas sufficiently large. The binary (yes/no) responsesserved as a measure for participants’ reward expecta-tions. It was expected that greater effort requirementswould decrease the share of participants for whom2 movie tickets would suffice, but would have noeffect regarding the 80 movie tickets (assuming these80 tickets are guaranteed). Participants also rated thedegree to which attaining the reward involved effortfor them, using the 11-point perceived effort scale dis-cussed earlier.

ResultsParticipants’ effort ratings confirmed that the manip-ulation affected the perceived effort in the expecteddirection. Specifically, a planned contrast indicated asignificant linear trend in the mean perceived-effortrating as a function of higher number of required sur-veys (p < 001; see Table 2). Moreover, as expected,the share of participants who indicated that the sure-small reward was sufficient decreased with both thenumber of required online surveys (see Table 2)and with the perceived-effort ratings (wald-�2 = 189,p < 0001; and wald-�2 = 263, p < 0001, respectively).It is noteworthy that there was no curvilinear effectof required surveys or perceived effort on the ten-dency to view the sure-small reward as sufficient. Fur-ther, as expected, the percentage of participants whoindicated that the large-uncertain reward was suffi-cient remained high (over 80%) across all requirementconditions. These results suggest that higher requiredefforts increased consumers’ reward expectations (andreference points) for evaluating the program rewards.

Table 2 Perceived-Effort Ratings and Reward Satisfaction in theOnline Survey Program

Mean Perceived- Percent Satisfied Percent SatisfiedNo. of Required Effort Rating with Sure-Small with Large-UncertainSurveys (0–10) Reward (%) Reward (%)

0 3�3 76 923 4�4 62 845 4�6 62 838 4�7 55 8510 4�9 54 8315 5�4 38 80



Figure 6 The Curvilinear Effect of Effort Requirements on Preferencefor Sure-Small over Large-Uncertain Rewards—The OnlineSurvey Program

69%67%

71%

80%

84%

79%

40%

50%

60%

70%

80%

90%

100%

0 3 5 8 10 15

Number of Required Online Surveys

Shar

e of

Sure

-Sm

allR

ewar

d

Consequently, greater effort requirements increasedthe chances that the sure-small reward would not suf-fice as a compensation, whereas the uncertain rewardwas apparently large enough to satisfy the rewardexpectations of most consumers across the range ofeffort requirements.

Hypothesis 4, which predicts an inverse-U effect ofeffort on the preference for the sure-small reward, wastested using a logistic regression; the independentvariables included the effort requirement level (0, 3,5, 8, 10, or 15 online surveys) and a (mean-centered)quadratic effort term. Consistent with Hypothesis 4,the quadratic term was significant and in the hypoth-esized direction �wald-�2 = 41; p < 005�, indicatinga significant curvilinear effect of effort. In particular,in the no-effort condition, the relative choice share ofthe sure-small reward was 69% (47 out of 68 partici-pants), whereas in the three and five online surveys(effort) conditions, the share of this reward increasedto 79% (42/53) and 84% (42/50), respectively. How-ever, when the effort requirements were further raisedto 8, 10, and 15 online surveys, the relative share ofthe sure-small reward declined to 80% (47/59), 71%(47/66), and 67% (34/51), respectively (see Figure 6).

To further examine the relationship between theeffort construct and consumers’ reward preferences,a logistic regression was used in which the indepen-dent variables were the 11-point perceived-effort rat-ings and a (mean-centered) quadratic perceived-effort

term. Consistent with Hypothesis 4, the quadraticperceived-effort term was statistically significantand in the hypothesized direction �wald-�2 = 39;p < 005�, indicating that the share of the sure-smallreward was an inverse U-function of the perceivedeffort.

The results also supported the prediction that thepreference for the sure-small reward would be weakerwhen completing (five) surveys is linked to a direct($50 per survey) monetary compensation. Specifically,whereas 84% of participants in the five-survey con-dition chose the sure-small over the large-uncertainrewards, only 62% (34/55) chose the certain rewardwhen completion of the five surveys also earned $250�t = 27�p < 0005�. Apparently, when consumers havea primary motivation for engaging in the efforts, theexpectation of (additional) FP rewards is attenuated,thereby increasing the tolerance of risk.

The Curvilinear Relationship Between Effort andPreference for Sure-Small Rewards: DiscussionBuilding on the notion that greater effort require-ments increase the expectation of reward, therebyinducing a shift in the reference used to evaluate theactual program rewards (Assumptions 1 and 2), it waspredicted that effort would have a curvilinear effecton the preference for sure-small over large-uncertainrewards. Specifically, as long as the sure-small rewardis sufficient relative to consumers’ reward expecta-tions, a higher reference point means that the con-siderable possibility (inherent in the large-uncertainreward) of not receiving any compensation wouldbe coded as a greater (aversive) loss. Therefore, theattraction of the sure-small reward, which eliminatesthe possibility of such a perceived loss, was predictedto increase with greater effort requirements. However,the effect of effort was expected to reverse once con-sumers perceived the sure-small reward as insuffi-cient relative to the effort-contingent expectation. Insuch a case, the large-uncertain reward offers the pos-sibility of escaping the increasing certain loss (i.e., dueto higher effort) inherent in the sure-small reward.Appendix A provides a formal proof of the curvilin-ear effect of effort based on this conceptualization andAssumptions 1 and 2.



The empirical evidence provides strong support forthe inverted-U hypothesis. In particular, the resultsof two studies that elicited FP choices with real con-sequences demonstrated that greater effort require-ments had a curvilinear effect on the preference forreward certainty. Process measures supported thenotion that the mechanism underlying this effectis the effort-induced shifts in the reward expecta-tions. In particular, the results of the online surveystudy showed that greater effort requirements (andperceived-effort) had a negative linear effect on thelikelihood of perceiving the sure-small reward as suf-ficient. The choice explanations (from Study 2) arealso consistent with the conceptual framework.

General DiscussionThe fruits of effort often vary in terms of their like-lihood and size. A fundamental question, then, iswhat determines preferences toward the certainty andmagnitude of effort-contingent rewards. The presentpaper investigates this question in the context ofFPs, which have been widely adopted by compa-nies and have received a great deal of attention frommarketers, consultants, and, to a lesser degree, aca-demics. Two simple assumptions are made: (1) Effortleads to reward expectations, and (2) the valuation ofactual rewards vis-à-vis the expectation is consistentwith the value function. The conjunction of these twoassumptions is shown to provide a parsimonious andunifying theory that predicts a wide range of findingsregarding the impact of effort on risky choice. Thissection briefly reviews the key results and discussestheir theoretical and practical implications for FPs andother types of incentive systems.

Key Findings and Theoretical Implications

Review of Key Findings. A series of stud-ies involving both real and hypothetical decisionsdemonstrated that the required effort stream influ-ences consumers’ trade-offs between the certainty andmagnitude of rewards. Specifically, it was shown that(a) the presence (as opposed to absence) of effortrequirements increases consumer preference for sure-small rewards over large-uncertain rewards (Study 1),and (b) when required efforts are further increased

the preference for sure-small reward reverses; thatis, the preference for sure-small rewards over large-uncertain rewards is an inverse U-function of theeffort level (Studies 4 and 5). These results were pre-dicted based on the conjunction of the two simpleassumptions mentioned earlier.

Process measures, including analyses of choiceexplanations and satisfaction with rewards, providedsupport for the idea that reward choices are moti-vated by effort-contingent expectations.9 Moreover, akey test of the conceptual framework involved exam-ining the impact of intrinsic motivation on rewardpreferences. It was posited that intrinsic motivationdecreases the expectation of extrinsic reinforcement,thus attenuating the impact of effort on FP rewardpreferences. Consistent with this analysis, Study 2demonstrated that individuals with high versus lowintrinsic interest in the required effort activity (e.g.,“math lovers” versus “math haters”) were less likelyto choose a sure-small reward over a large-uncertainreward. Study 3 further tested this account by manip-ulating rather than measuring participants’ intrinsicmotivation. And, as expected, the results demon-strated that the positive impact of effort (comparedto a no-effort condition) on the relative preference forsure-small rewards was weaker for an effort activitythat was intrinsically motivating (enjoyable) than fora similar activity that was not motivating.

The curvilinear effect of effort on the trade-offbetween the certainty and magnitude of rewardsand the moderation of this relationship by intrin-sic motivation are consistent with the conceptualiza-tion of shifts in the reference point. Of course, theremay exist other (complementary) frameworks that canaccount for a subset of the findings. For instance,self-perception theory (Bem 1967), which provides thefoundation for the literature on intrinsic motivation(see, e.g., Lepper and Greene 1978), can help accountfor the moderating role of intrinsic motivation. Inaddition, the sunk-cost effect (e.g., Arkes and Blumer1985, Thaler 1980, Zeelenberg and van Dijk 1997) isrelated to the finding that the anticipation of future

9 This conclusion was further supported by an analysis of the choiceexplanations provided in the grocery and hotel problems (Study 1).Detailed results can be obtained upon request.



effort (as opposed to a lack of such anticipation)increases choices of sure-small rewards over large-uncertain rewards. Nevertheless, the wide range offindings regarding the complex effects of effort andintrinsic motivation on risky choice cannot be easilypredicted by such alternative accounts.

It is important to note that these findings haveimportant implications that extend beyond FPs. First,the basic structure of an effort stream that leads to(potential) future rewards is ubiquitous (e.g., othertypes of motivational incentive systems). Second,choice between (risky) outcomes or rewards is oftencontingent on effort. Third, the analysis of shifts in thereference point is more general than the particular, yetimportant, case of effort-contingent rewards. Specif-ically, the neutral reference point can be influencedby multiple other factors besides effort (see alsoKahneman and Tversky 1979, Thaler and Johnson1990). The present paper provides a systematic anal-ysis of the effects of reference shifts on risky choice.This analysis includes a formal proof (shown inAppendix A) that specifies the boundary conditionsunder which the conjunction of a reference shift withthe properties of the value function can account forthe observed findings. Such conditions relate to therelative location of the reference point and the offeredrewards (or outcomes), the coefficient of loss aversion,and the probability of winning the rewards. Futureresearch can build on this theoretical analysis, forinstance, by estimating and validating the reference-dependent model of Appendix A and by generaliz-ing the framework to account for the effects of othercosts and investments besides effort (e.g., expendingmoney, time, or information; tolerating physical pain).

Antecedents and Consequences of Effort-InducedReward Expectations. The notion that consumers’choice of rewards is contingent on the level and typeof required effort can be seen as another illustra-tion of the construction of preferences (e.g., Bettmanet al. 1998, Payne et al. 1992). Here, consumers appearto evaluate rewards relative to an effort-inducedreward expectation that serves as a malleable ref-erence point. This conceptualization is related to agrowing body of diverse research on the reference-and context-dependence of consumer choice (e.g.,Heath et al. 1999, Hoch and Loewenstein 1991, Prelec

and Loewenstein 1998, Simonson and Tversky 1992,Thaler 1985, Tversky and Kahneman 1991, Winer1986). The present paper sheds light on the importantyet under-researched issue of how consumers con-struct reference points, and highlights the key role ofeffort.

A question that naturally arises is what factorsinfluence the degree to which effort requirementsaffect the reward expectation (or reference point).The present research has underscored one such mod-erator, namely the level of intrinsic motivation forengaging in the required effort activity. Specifically,higher intrinsic motivation weakens the expectationof extrinsic reward and consequently attenuates theeffect of effort on reward choice. Relatedly, the expec-tation of FP rewards is likely to be lower when theserewards serve as the secondary rather than primarymotivation for engaging in the effort stream. Supportfor this conjecture was found in Study 4 (online sur-vey program), in which the preference for a sure-smallover a large-uncertain reward was significantly lowerwhen consumers received an additional direct com-pensation ($50/survey) for their efforts (completingfive online surveys).

Moreover, some consumers may intrinsically valuethe effort activity so much that the effort requirementsdo not increase their reward expectations, but rathermay even decrease them (e.g., movie aficionados whoare asked to preview and critique unreleased films).For these consumers, the effort requirements may leadto a “negative” reward expectation (i.e., a left shiftin the neutral reference point), consequently enhanc-ing their risk tolerance. Essentially, a left shift in thereference point implies that the prospect of no (FP)reward is still coded as a gain relative to the “nega-tive” reward expectation. Consistent with this concep-tualization, participants in the online survey programchose the large-uncertain reward more often whenthey were required to complete five surveys for an(exaggerated) fee of $250 than when they received aneffort-free reward.

Future research can examine whether the framingof the program and its communications can lowerthe (reference) reward expectation, for example, bysuggesting that consumers are lucky to be selectedfor an exclusive program. Relatedly, because extrinsic



rewards may distract consumers from their intrinsicmotivations (e.g., Deci and Ryan 1985, Lepper 1981),consumers may be more likely to invest effort whenno (extrinsic) reward is offered compared to whenan inadequate (i.e., too small or unlikely) rewardis provided. The antecedents and consequences ofreward expectations raise a variety of other importantand interesting conceptual questions relating to suchissues as (1) whether obtaining the reward was theintention or rather an incidental by-product of invest-ing the effort, (2) whether the choice of rewardis performed before or after complying with theeffort requirements, and (3) whether the consumer isin a prevention or promotion regulatory focus (seeHiggins 2002).

Effort-induced reward expectations also haveimportant implications for consumers’ sensitivity (orresponsiveness) to the magnitude of sure rewards(i.e., rewards that are guaranteed upon completionof the required effort activity). In a differentpaper (Kivetz 2003), it is shown that greater effortrequirements increase the positive impact of (or sen-sitivity to) larger (sure) rewards. This finding is con-sistent with the conjunction of Assumptions 1 and 2(due to higher effort), because the concavity of thegain function implies that increasing the referencepoint will enhance the perceived difference between(sure) rewards of varying magnitudes. It is notewor-thy, however, that consumers should (normatively)care less about the magnitude of the reward whenthe required effort is high, because higher effortimplies lower probability (and frequency) of complet-ing the program and reaching the reward. Indeed,Kivetz (2003) demonstrates that when consumers areprompted to consider their likelihood of completingthe program, higher required effort decreases the sen-sitivity toward the magnitude of the reward.

Practical ImplicationsBeyond the theoretical significance of understand-ing the impact of effort on preferences towardthe certainty and magnitude of rewards, this issuehas important practical implications for frequencyprograms and other types of incentive systems. Theadvent of the Internet and other new technologies

(e.g., CRM software) has led to a proliferation of pro-grams that reward consumers for the investment ofvarious efforts, including reviewing products, com-pleting surveys, shopping, exercising, gambling, andmore. These myriad FPs offer different types andmagnitudes of rewards, including uncertain ones.Nevertheless, as several FP experts have argued,many of these programs are structured with a limitedunderstanding of consumer preference (e.g., Barlow1999, O’Brien and Jones 1995). Although a completeunderstanding of the determinants of FP successrequires a great deal of additional study, the presentresearch provides insights regarding the matching ofrewards with efforts and the design, promotion, andtargeting of FPs.

With respect to the design of FPs, the findingsimply that, as the level of program requirementsincreases, marketers should vary (in a nonlinear way)the relative share of sure-small versus large-uncertainrewards in their “reward mix.” Marketers can alsooffer simultaneously two or more FPs, with eitherdeterministic or stochastic reward systems and differ-ent levels of program requirements. Furthermore, astraightforward implication of the present research isthat when the effort activity is not inherently motivat-ing, marketers should refrain from relying solely onprobabilistic reward systems. Indeed, even the Inter-net portal iWon, famous for its use of sweepstakesentries as an incentive for Web site browsing, hasrecently extended its program by also offering pointsthat are redeemable for sure rewards.

The findings of this research provide some gen-eral guidelines regarding the manner in which FPscan be promoted and targeted. For example, byemphasizing the intrinsic value of the effort activ-ity and the secondary role of the program rewards,and by targeting programs toward highly motivatedindividuals, marketers may be able to reduce the pro-gram’s funding rate (the reward-to-effort ratio) with-out a significant drop in participation rates. Althoughexisting FPs do not permit a rigorous test of thisimplication, there are indications that various pro-grams were able to lower their funding rates byusing related tactics—for instance, by stressing thepleasure of rating music (Moodlogic, Inc.) or thebenefits of voicing one’s opinions and learning how



they compare with others’ opinions (HarrisPollOnlineRewards) over the extrinsic rewards of the program.Relatedly, FPs can increase the intrinsic motivation ofparticipants (thus deemphasizing the need for costlyrewards) by providing identity-related “soft” bene-fits (see, e.g., Lind and Tyler 1988) such as rankingand congratulating top members, fostering a sense ofcommunity, and treating members as unique, valu-able individuals.

Finally, the present research may provide insightsregarding other types of incentive systems, suchas employment contracts, sales force compensationplans, and even academic tenure tracks. For exam-ple, salespeople can often earn cash bonuses or non-monetary rewards for reaching a specific sales quota.Understanding the relationship between efforts andpreferred rewards may improve the design of suchbonus plans. Further, interestingly, the compensationstructure of workers in intrinsically motivating pro-fessions (e.g., athletes, artists, politicians) is oftenstochastic, whereas that of laborers in low intrin-sic motivation occupations is invariably determinis-tic (e.g., sanitary workers, prison guards). The exten-sion of the present research to labor market psycho-logy and economics is an interesting avenue for futureresearch.10

Let us conclude by noting the advice often given tojunior professors—“just enjoy your research!” Indeed,given the uncertainty inherent in the outcome ofthe research process (e.g., publications and tenure),focusing on the intrinsic rewards of scholarship isa good way to reduce any possible perceptions ofloss and disappointment due to insufficient extrinsicrewards.

AcknowledgmentsThe author is grateful to Yuhuang Zheng for his helpful sugges-tions and research assistance and to Jukay Hsu and the faculty ofStuyvesant High School for their help in conducting Study 2. Thispaper benefited from the comments of Sunil Gupta, Yifat Kivetz,Oded Koenigsberg, Donald Lehmann, participants in the Chicago,Columbia, and MIT seminars, and from the Marketing Scienceeditor, area editor, and reviewers. This research was supported inpart by a research grant from the Institute for Social and EconomicResearch and Policy.

10 The author is grateful to Eric Johnson and Drazen Prelec forrelated discussion.

Appendix A: Formal Proof of the ConceptualFramework11

This appendix shows that the conjunction of two simple assump-tions provides a unifying framework for the findings of the presentpaper regarding the impact of effort on reward preferences. Thetwo assumptions are:

(1) effort requirements create an expectation for reward (i.e., areference point for evaluating the actual FP rewards), with higherrequirements leading to greater expectations; and

(2) the valuation of program rewards vis-à-vis the rewardexpectation (or reference point) follows the principles of prospecttheory’s value function (i.e., reference-dependence, loss aversion,and diminishing sensitivity).

Thus, in the subsequent analyses, vE�x� is the subjective value ofoutcome x given a reference point rE , where the reference point rE(equivalent to the expected fair reward) increases with greater effortrequirements E. Diminishing sensitivity implies that, for x > rE ,v′′

E�x� < 0, whereas for x < rE , v′′E�x� > 0. Further, following Tversky

and Kahneman (1991), it is assumed that the value function exhibitsconstant loss aversion, captured by the loss-aversion coefficient, �.Thus, the reference-dependent value function can be expressed as

vE�x� =

g�x− rE� if x ≥ rE

�−��g�rE −x� if x < rE�

where g�0� = 0, g′ > 0, g′′ < 0, g′′′ ≥ 0, � > 1, and rE increases ineffort.12

Proposition 1 (Hypothesis 1). As long as the sure-small rewardsatisfies the reward expectation (i.e., s ≥ rE), and the probability of win-ning the large-uncertain reward is reasonably low (i.e., pl < p̂l), the pref-erence for sure-small rewards over large-uncertain rewards will increasewhen the rewards are contingent on effort �rE > 0� compared to when therewards are effort free �rE = 0�. When � = 2, p̂l = 05.

Note that the sure-small reward (S) is a riskless prospect thatoffers s with probability 1. Conversely, the large-uncertain reward(LU) yields outcome l with probability pl (where pl < ps = 1 andl > s ≥ rE) and outcome 0 with probability 1−pl. Given a reference

11 The author is indebted to Oleg Urminsky for his invaluable inputand contribution to this proof.12 The assumption that g′′′ ≥ 0 (i.e., convexity of marginal utility)ensures nonincreasing risk aversion (see Pratt 1964) and is consis-tent with a power function formulation for the value function asproposed by Tversky and Kahneman (1992) and estimated in theirand other studies (e.g., Camerer and Ho 1994, Donkers et al. 2001,Wu and Gonzalez 1996).



point rE , we have the following reward valuations (V ):13

V �S � rE� = g�s− rE� versus

V �LU � rE� = pl ∗g�l− rE�− ��∗ �1−pl�∗g�rE��

For any pair of sure-small and large-uncertain rewards that sat-isfy the above conditions, we define the relative preference for (oradvantage of) S over LU, given a reference point rE , as A(S, LU� rE).Thus,

A�S, LU � rE� = V �S � rE�−V �LU � rE�= g�s−rE�−pl ∗g�l−rE�+ ��∗�1−pl�∗g�rE��

14

We wish to examine the impact on A�S�LU � rE� of increasingthe reference point from zero to rE > 0 (i.e., making the rewardscontingent on effort E rather than no-effort). The change in thecomponents of A�S�LU � rE� as the reference point shifts from 0 to rE(where s ≥ rE > 0) can be written as

�g�s� = g�s− rE�−g�s−0� = g�s− rE�−g�s� < 0�

�g�l� = g�l− rE�−g�l−0� = g�l− rE�−g�l� < 0�

�g�rE� = g�rE�−g�0� = g�rE� > 0

Thus, the change in A�S�LU � rE� as the reference increases fromzero to rE can be expressed as

�A�S, LU � rE� = A�S, LU � rE�−A�S, LU � 0�

= �g�s�−pl ∗�g�l�+ ��∗ �1−pl�∗g�rE��

It is proposed that there exists a p̂l such that �A�S, LU � rE� > 0 forall pl < p̂l. To identify p̂l, we search for the smallest pl that satisfiesthe inequality: �A�S, LU � rE� > 0.

Solving for pl, we get,

�g�s�−pl ∗�g�l�+�∗g�rE�−�pl ∗g�rE� > 0�

pl ∗ ��g�l�+�∗g�rE�� < �g�s�+�∗g�rE�

Because g is strictly concave and g�0�= 0, g�s− rE�+g�rE� > g�s�

and g�l− rE�+ g�rE� > g�l� (see Lemma 1). Therefore, �g�s�+ � ∗

13 In this and the subsequent analyses, consumers are assumedto adopt the explicit probabilities (i.e., p) stated for the variousrewards. Replacing these probabilities with prospect theory’s deci-sion weights (i.e., ��p�) does not alter the nature or conclusions ofthe analyses.14 The relative advantage of S over LU (i.e., A), which equals the dif-ference in their utilities, can be used to compute the probability ofchoosing S over LU by employing a “single-agent stochastic choicemodel” (see Camerer and Ho 1994). Such a model assumes a singlepreference structure for all consumers (the deterministic componentof utility), and an additional random utility component that leadsto variations in consumers’ choices (for further details see Camererand Ho 1994).

g�rE� > 0 and �g�l�+ � ∗ g�rE� > 0 whenever � > 1. Because bothterms are positive, the inequality can be rewritten as

pl < ��g�s�+�∗g�rE��/��g�l�+�∗g�rE��

Thus, we are searching for p̂l = Min��g�s�+� ∗ g�rE��/��g�l�+� ∗ g�rE�� . This p̂l is minimized when �g�s� < 0 is at its mini-mum and �g�l� < 0 is at its maximum. By definition, Min�g�s� =Min�g�s− rE�−g�s��. We have noted above that because g is strictlyconcave and g�0� = 0, g�s − rE� + g�rE� > g�s�, and therefore,g�s− rE�−g�s� > −g�rE�. Thus, Min�g�s� →−g�rE�. The maximumof �g�l� is less than zero, because �g�l� = g�l − rE� − g�l� < 0.Therefore,

pl < �−g�rE�+�∗g�rE��/�0+�∗g�rE�� = ��−1�/�

Thus, p̂l = ��−1�/�, and consequently, for all pl < p̂l, �A > 0.Moreover, based on empirical evidence (e.g., Heath et al. 1999;

Kahneman et al. 1990; Tversky and Kahneman 1991, 1992), it isassumed that �≥ 2. In the specific case, �= 2, we have p̂l = 05. �

Proposition 2 (Hypothesis 4). Assuming � ≥ 2 and pl < 05,there exist r∗ < r∗∗ (where s/2 < r∗ ≤ s), such that:

• When 0 ≤ rE < r∗, !A/!rE > 0.• When r∗ < rE , !A/!rE < 0 ( for all rE < r∗∗).

Equivalently, as long as rE < r∗∗, the advantage A(S, LU � rE) is a curvilin-ear (i.e., inverse-U shape) function of the required effort level (or referencepoint, rE), with a peak at r∗ (where s/2 < r∗ ≤ s).

Corollary 1. For any pl, r∗∗ > �l+ s�/2 > s.

Corollary 2. r∗∗ shifts to the right, toward l, as the probability pl

decreases (where 0 < pl < 1). Further, when pl → 0, r∗∗ →�.

Proposition 2 is demonstrated in three steps. First, it is shown:

Proposition 2a. If pl < p̂l (where p̂l = ��− 1�/�), then r∗ > s/2.When � = 2, p̂l = 05.

Consider 0 ≤ rE ≤ s/2. We want to show that in this range A

increases in rE . This can be expressed as the partial derivative A′ =!A/!rE > 0. Thus, we want to show that:

A′ = −g′�s− rE�+pl ∗g′�l− rE�+�∗ �1−pl�∗g′�rE� > 0

Because rE ≤ s/2, s− rE ≥ rE and g′�s− rE� ≤ g′�rE�. Therefore, wecan write g′�rE� = b ∗g′�s− rE� where b ≥ 1. Thus:

A′ = −g′�s− rE�+pl ∗g′�l− rE�+�∗ �1−pl�∗ b ∗g′�s− rE�

= pl ∗g′�l− rE�+ ��∗ �1−pl�∗ b−1�∗g′�s− rE�

Because g′�l− rE� > 0 and g′�s − rE� > 0, we have A′ > 0 if � ∗�1− pl� ∗ b− 1 ≥ 0, or equivalently, if � ∗ �1− pl� ∗ b ≥ 1. Given thatb ≥ 1, it suffices to show that �∗ �1−pl�−1 ≥ 0 to show that A′ > 0.This is true when �−�∗pl ≥ 1, or equivalently, when pl ≤ ��−1�/�.Because we defined p̂l = ��− 1�/�, for all pl < p̂l, A′ > 0 (i.e., A isstrictly increasing) for any rE ≤ s/2. Thus, r∗ > s/2.

Assuming � = 2 (e.g., Tversky and Kahneman 1991), we havep̂l = 05. Note that p̂l increases with higher �.

Next, we show that:

Proposition 2b. For any pl, r∗ ≤ s.



Consider s < rE < �l + s�/2. By concavity, g′�rE − s� > g′�rE�.Because rE < �l + s�/2, we can show rE − s < l − rE . Therefore,g′�rE − s� > g′�l− rE�.

We want to show that A′ < 0. Because s < rE , this can be rewrit-ten as: A′ = −�∗g′�rE − s�+pl ∗g′�l− rE�+�∗ �1−pl�∗g′�rE� < 0, orequivalently:

−�∗g′�rE − s� < −pl ∗g′�l− rE�−�∗ �1−pl�∗g′�rE��

g′�rE − s� > �pl/��∗g′�l− rE�+ �1−pl�∗g′�rE�

Because � > 1, it suffices to show: g′�rE − s� > pl ∗ g′�l− rE�+�1−pl� ∗ g′�rE�. This must be true for any pl, because g′�rE − s� >

g′�rE� and g′�rE − s� > g′�l− rE�.Thus, as rE increases past s (toward l), A declines, and therefore,

r∗ ≤ s.Next, in order to complete the proof of Proposition 2, it remains

to show that:

Proposition 2c. For any pl, if s/2 < rE < s, then A′ = 0 holds at nomore than one point rE = r∗.

Because A′ > 0 for rE < s/2 and A′ < 0 for rE > s, and A′ is contin-uous in the range �s/2� s�, then either A′ > 0 for all rE < s, or theremust exist some point r∗ at which A′ = 0.

If A′ > 0 for all rE < s, then r∗ = s is the only local maximum inthe range �0� r∗∗�.

If, on the other hand, there exists some point r∗ at which A′ = 0,then we will show that point r∗ is unique. Consider any other pointr+ = r∗ +�r , where �r > 0 and s/2 < r+ < s. At this point r+, theslope is

A′ = −g′�s− r+�+pl ∗g′�l− r+�+�∗ �1−pl�∗g′�r+�

We know that, by definition, at r∗:

A′ = −g′�s− r∗�+pl ∗g′�l− r∗�+�∗ �1−pl�∗g′�r∗� = 0

So, we can subtract, and express the slope at r+ as

A′ = −g′�s− r+�+pl ∗g′�l− r+�+�∗ �1−pl�∗g′�r+�

− �−g′�s− r∗�+pl ∗g′�l− r∗�+�∗ �1−pl�∗g′�r∗��

A′ = −�g′�s− r+�−g′�s− r∗��+pl ∗ �g′�l− r+�−g′�l− r∗��

+�∗ �1−pl�∗ �g′�r+�−g′�r∗��

Because �r > 0, r+ > r∗. Therefore, the three terms of A′ are

(1) −�g′�s− r+�−g′�s− r∗�� < 0�

(2) pl ∗ �g′�l− r+�−g′�l− r∗�� > 0� and

(3) �∗ �1−pl�∗ �g′�r+�−g′�r∗�� < 0Because g′′′ ≥ 0, g′ is convex, and the rate of change of g′ is

nonincreasing. Therefore, given s < l, the rate of change in g′ ats− r∗ is greater than or equal to the rate of change in g′ at l− r∗.Thus, g′�s− r+�−g′�s− r∗�≥ g′�l− r+�−g′�l− r∗�. This implies that:

−�g′�s− r+�−g′�s− r∗��+pl ∗ �g′�l− r+�−g′�l− r∗�� ≤ 0. Because �∗�1−pl�∗ �g′�r+�−g′�r∗�� < 0, we have shown that A′ < 0 for r+ > r∗.

Alternatively, consider �r < 0. Then r− = r∗ +�r < r∗, and thethree terms of A′ are

(1) −�g′�s− r−�−g′�s− r∗�� > 0�

(2) pl ∗ �g′�l− r−�−g′�l− r∗�� < 0� and

(3) �∗ �1−pl�∗ �g′�r−�−g′�r∗�� > 0

Because g′′′ ≥ 0, and s < l, the rate of change in g′ at s − r∗

is greater than or equal to the rate at l − r∗. Thus, g′�s − r−�−g′�s− r∗� ≤ g′�l− r−�− g′�l− r∗�. This implies that: −�g′�s − r−�−g′�s − r∗�� + pl ∗ �g′�l − r−� − g′�l − r∗�� ≥ 0. Because � ∗ �1 − pl� ∗�g′�r−�−g′�r∗�� > 0, we have shown that A′ > 0 for r− < r∗.

Thus, we have shown that r∗ exists and is unique. �

Corollary 1. For any pl, r∗∗ > �l+ s�/2 > s.

This follows directly from the proof of Proposition 2b.

Corollary 2. r∗∗ decreases in pl (where 0 < pl < 1 and r∗∗ ≤ l).

Consider l ≥ r∗∗ > �l+ s�/2. Let rE = r∗∗. Because rE > �l+ s�/2, weknow that rE > rE −s > l−rE . Therefore, g′�rE� < g′�rE −s� < g′�l−rE).We also know that at rE = r∗∗, A′ = 0. We can rewrite this as � ∗g′�rE − s�= pl ∗g′�l− rE�+�∗ �1−pl�∗g′�rE�. Because pl + �1−pl�= 1and � ∗ g′�rE − s� > � ∗ g′�rE�, this can only be true if g′�l− rE� >

�∗g′�rE − s�, which implies that g′�l− rE� > �∗g′�rE�.Let us now decrease pl by some amount k, where 0 < k < pl. The

new slope of A at rE is expressed as

A′ = −�∗g′�rE − s�+ �pl −k�∗g′�l− rE�+�∗ �1−pl +k�∗g′�rE�

= �−�∗g′�rE − s�+pl ∗g′�l− rE�+�∗ �1−pl�∗g′�rE��

+k∗ ��g′�rE�−g′�l− rE��

We know that, given pl, �−�∗g′�rE−s�+pl ∗g′�l−rE�+�∗�1−pl�∗g′�rE�� = A′�rE = r∗∗� = 0. Therefore, if pl is decreased by k, thenA′ = 0+k ∗ ��∗g′�rE�−g′�l− rE��. Further, it was shown above thatg′�l− rE� > � ∗ g′�rE� and we chose k > 0. Hence, A′ < 0, and wehave shown that r∗∗ shifts to the right, toward l, as the probabilitypl decreases.

Next, it is shown that when pl → 0, r∗∗ → �. By Corollary 2,decreasing pl increases r∗∗. In the limit, pl → 0, implies A′ → −�∗g′�rE − s�+ � ∗ g′�rE�, which can be rewritten as A′ → � ∗ �g′�rE�−g′�rE − s�� < 0, and A declines continuously. Note that A is contin-uously differentiable in the interval �s��. Therefore, we can saythat in the limit, as pl approaches 0� r∗∗ approaches infinity. �

Lemma 1. Under strict concavity of function f , assuming f �0�= 0�f �a+b� < f �a�+f �b�. Assume, without loss of generality, that 0 <a< b

By strict concavity, f �a+b� < f �b�+a∗f ′�b�. We will show that f �a� >

a∗f ′�b�.Note that for any 0 < a < b� a∗f ′�a� > a∗f ′�b�. It now remains to be

shown that f �a�≥ a∗f ′�a�. For any 0 < x ≤ a, f ′�a�≤ f ′�x�⇒ a∗f ′�a�≤∫ a

0 f ′�x�dx = f �a�− f �0� = f �a�.⇒ f �a� ≥ a∗f ′�a� > a∗f ′�b�, and we have proved that f �a+ b� <

f �a�+ f �b�.



Appendix B: Additional Tests of Hypothesis 1Grocery Store Scenario—Effort Condition:

Grocery Store Rewards

Imagine that your grocery store offers its frequent customers the opportunity to earn one of the following two rewards:

Reward A: After you purchase groceries at the grocery store five times (each purchase must be over $30), you will earn a 1/50 chanceto win a $1,000 grocery certificate good toward future grocery purchases (one out of every 50 participants wins).

Reward B: After you purchase groceries at the grocery store five times (each purchase must be over $30), you will earn a $15 grocerycertificate good toward future grocery purchases.

Circle the reward you would prefer to earn: A B

Grocery Store Scenario—No-Effort Condition:

Grocery Store Rewards

Imagine that as an appreciation gift your grocery store offers a choice between the following two rewards:

Reward A: A 1/50 chance to win a $1,000 grocery certificate good toward future grocery purchases (one out of every 50 participantswins).

Reward B: A $15 grocery certificate good toward future grocery purchases.

Circle the reward you would prefer to receive: A B

Hotel Scenario—Effort Condition:

Hotel Frequency Program

Imagine that a luxury hotel chain offers guests the opportunity to earn one of the following two rewards:

Reward A: If you stay 10 nights (not necessarily on one occasion) at the chain’s hotels, you will earn a $100 cash award (the awarddistribution takes place one week after you accumulate 10 nights).

Reward B: If you stay 10 nights (not necessarily on one occasion) at the chain’s hotels, you will earn an entry into a lottery with a1/1,000 chance to win a $100,000 cash award (one out of every 1,000 participants wins; the lottery and award distributiontake place one week after you accumulate 10 nights).

Circle the reward you would prefer to earn: A B Wouldn’t join this program

Hotel Scenario—No-Effort Condition:

Hotel Raffle

Imagine that a luxury hotel chain offers guests the opportunity to win one of the following two rewards in a free raffle:

Reward A: If you win the raffle, you will receive a $100 cash award (the award distribution takes place one week after you win theraffle).

Reward B: If you win the raffle, you will receive an entry into a lottery with a 1/1,000 chance to win a $100,000 cash award (one outof every 1,000 participants wins; the lottery and award distribution take place one week after you win the raffle).

Circle the reward you would prefer to receive: A B Wouldn’t want either reward



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This paper was received December 10, 2002, and was with the authors 1 month for 1 revision; processed by Joel Huber.


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