individual learning in different social contexts

The Journal of Socio-Economics 36 (2007) 15–35

Individual learning in different social contexts

Marco Novarese ∗Centre for Cognitive Economics, Universita del Piemonte Orientale,

Corso Borsalino 44, 15100 Alessandria, Italy

Abstract

This paper analyses the effects of learning on individual behaviour in an experiment that requires coopera-tion and coordination within teams. Different social contexts were created and used as training environmentsfor artificial agents. The results confirm previous findings (on the tendency to repeat successful strategies andto apply them in new situations) and suggest new hypotheses. Learning is based not only on a mechanicalrepetition of past choices, but also on the attitude toward building a model of the world. Moreover, the paperempirically tests the role of satisfaction in routinization.© 2006 Elsevier Inc. All rights reserved.

JEL classification: C9; D81; D83

Keywords: Learning; Coordination; Cooperation; Cognitive economics; Experiments

1. Introduction

This paper analyses the effects of different kinds of training on individual behaviour in anexperiment that requires cooperation and coordination within teams. From a general point ofview, the present work is a contribution to the approach that I have elsewhere defined as cognitiveexperimental economics (Novarese, 2003a): it is a part of the wider stream of analysis calledcognitive economics (Egidi and Rizzello, 2003). The focus of this area of research, at the crossroadsof the heterodox tradition and cognitive sciences, is on the study of individual and organizationallearning, which is seen as a key factor in shaping social phenomena.

Because of these roots, the definition of learning differs from that of mainstream economics,where such mechanisms are used to explain of the human ability to make rational decisions (Perez,2000): individuals are not able to maximize, but learn to converge towards optimal solutions.Learning is therefore a mechanism that assists error-reduction in decision-making. Cognitive

∗ Tel.: +39 0131 283753; fax: +39 0131 56808.E-mail address: [email protected]: http://www.novarese.org.

1053-5357/$ – see front matter © 2006 Elsevier Inc. All rights reserved.doi:10.1016/j.socec.2005.12.013

16 M. Novarese / The Journal of Socio-Economics 36 (2007) 15–35

psychology proposes a more general view and defines learning as any modification in humanbehaviour related to the experiences of the individual.

This difference is also mirrored in the experimental analysis. If, in the traditional view, learningis often seen as a possible solution for the irrational behaviour observed, in the cognitive approach,on the contrary, it is one of the factors that can explain it. Egidi and Narduzzo (1997), for example,showed that, when individuals develop a successful routine in a given environment, they apply italso in different contexts, where it might turn out to be inefficient.

The results proposed here confirm such findings, but use a new and different context. Atthis stage, finding similar results in different experiments is very important, for it reinforces theresults of recent research. Furthermore, the present work expands knowledge and suggests newhypotheses to be investigated further on issues such as the effects of learning in an environmentcharacterized by different levels of fairness and difficulty, and on the role of satisfaction in suchprocesses.

The experimental game proposed here presents some similarities with “Target the two” pro-posed by Cohen and Backdayan (1991) and later by Egidi and Narduzzo (1997) for studyingorganizational learning. Its main novelty is that here the agents’ interests are partly counterposedas someone has to pay a higher cost than the others. This makes coordination more difficult, butit also allows the situation to be represented more realistically. As emphasized by Cohen et al.(1996, p. 670) organizational routines often “emerge and operate in a universe of . . . conflict anddiverging interests”. This is why it is important to study their origin.

The game “Sum 10” described in the next section represents, therefore, a metaphor of variousstrategical situations characterized by the following conditions:

- There are many possible outcomes, more or less efficient for the group as a whole (for examplea given good, produced by a firm, can be of top quality or second best).

- A certain level of coordination is necessary to reach any of the possible outcomes.- The division of labour is not centrally planned.- Individuals can contribute in different ways, and it is necessary that someone provides a greater

level of effort than the others.

Situations of this kind are widespread in the real world at a social and organizational level. Teamperformance emerges from the choices of a number of individuals whose behaviour is interrelated.Therefore, both coordination and cooperation are involved, and there are many possible outcomes.Yet, these kinds of interaction are usually neglected by economic analyses (both theoretically andempirically) because of their complexity, and economic theory takes into account only simplesituations.

Experimental economics maintains, generally, the same approach, because of the need to buildenvironments that can be easily analysed and which are under the researcher’s control. Besides,it is strongly dependent on theory (even when criticising it). For this reason, experiments aregenerally based on theoretical situations, and they aim to test or compare competing models.

Also the game proposed here is, obviously, a stylized situation. Yet, it is more complex thanthe usual experimental games and it aims at studying, at an empirical level, how to complicateeconomics. This task requires both a new approach of analysis (new variables to be taken intoaccount, for example), and new statistical and empirical tools (for example, how can we testhypotheses in an emergent situation like this, in which there is no independence among individu-als?). After understanding the basic feature of this game and how to analyse it, it will be possibleto develop different and more realistic versions.

M. Novarese / The Journal of Socio-Economics 36 (2007) 15–35 17

From a traditional point of view, “Sum 10” can be seen as too difficult to control as it involvesboth cooperation and coordination, which are usually studied in separate games. Besides, agentsare allowed too many choices compared to typical experiments (like, for example, the classicalprisoner’s dilemma). In fact, one of the aims of this work is testing the possible effects of learning ina context characterized by different levels of cooperation, and the relevance of repetitive behaviour.

The next section presents background literature related to the many sides of “Sum 10”. Thisincludes the theory of the firm and organization, the studies of the evolution of focal points, andthe analysis of human learning. The focus of the empirical analysis proposed here is on only thislast aspect. The following two sections describe the experiment and its results, respectively. Thelast section discusses the main findings.

2. The background literature: rationality, learning and fairness

This paper contributes to the cognitive approach and rejects the mainstream view on individualdecision-making as a maximization process. Because of the lack of some relevant informationand because of the need to conserve mental effort, individuals are not able to make fully rationaldecisions. Simon (1976) replaced the idea of optimization with that of satisficing.

According to this different view, individuals are likely to make a decision if it allows reachinga given level of satisfaction. Later, they will repeat the same action if it has proved to be successfulin the past, and to change it, if it has not. In this way, when a problem is solved in a satisficing way,behaviour tends to become routinized. So, the processes of learning arising from the describedmechanism, cannot be seen as a walk towards optimality (as, for example, in Sargent (1993)), butas an intent on the part of individuals to modify their behaviour, in a more or less permanent way,whenever new experience is acquired.

Routinization, as a result of learning processes, is an inborn characteristic of human beings,useful to reduce mental effort and to lower the uncertainty of the environment, but it can lead tosub-optimal strategies (see Egidi and Narduzzo (1997) for an example). This kind of mechanismhas been analysed and modelled in different ways, through various types of reinforcement andpath-dependent mechanisms. It is not possible to analyse and review them here (see, for example,Egidi and Rizzello, 2003; Roth and Erev, 1998; Charness and Levin, 2003; Slembeck, 1999).Nevertheless, in relation to the cognitive view, it is necessary to note the following:

(a) Individuals differ in regard to various behavioural traits. Personality variables matter inexplaining the individual behaviour in different situations (especially in ‘weak’ as opposedto ‘strong’ ones, as showed by Weiss and Adler, 1984). This conclusion emerges, more orless directly, from many papers, and it should be studied further. In relation to the experimentproposed here, two individual differences should be held in mind: (i) the attitude towardsone’s own and the other players’ opportunism and (ii) the tendency to routinize behaviour.

(b) Human learning cannot be reduced to a simple repetition of successful actions, as humanbeings have the ability to think about what has happened, to imitate others, and to comparetheir situation with that of their neighbours. They also have the capacity for reflecting on thepossible choices of the partners involved in strategic situations. Individuals tend, in fact, tobuild models of the world.

Learning should, therefore, be seen as the broad process that is engaged in to define suchrepresentation of the reality. Later, these models are applied also to contexts that differ from theone in which they have been developed (Egidi, 2002). For this reason, people show repetition, as


observed in many experiments. Yet, in other cases, there are more complex reactions that cannotbe modelled by simple reinforcement algorithms. The construction of this (cognitive) model isnot easy, and it requires additional empirical evidence. This is one of the aims of the present paper.

The picture of the world created by human beings – in strategic situations like “Sum 10” – isnecessarily linked to their ideas of fairness and justice, which are an important determinant of theirbehaviour. There is an extensive literature on this issue (see Novarese (2003b) for more details),but with few definite conclusions, for the disparity in results presented by empirical studies makeit difficult to draw a general picture. This is probably due to the following determinants:

- The wide variety of factors that influence reciprocal trust and the decision of being an egoist oran altruist.

- The role that is played by the differences in personal characteristics (see Boone et al., 1999)and in the perception of the situations. So, according to the situation, individual players canreact in different ways when facing opportunism.

- In many cases they might accept losses (or low payoffs) to punish the free riding of others. Inthis case, emotions play an important role (Frank, 1988).

- If the disparity is not too high (or the absolute value of the payoff sufficiently higher), someplayers’ behaviour is more rational: it is better to win less than to win nothing.

- Unfair solutions can be accepted for different and specific reasons. For example, unfair solutionssometimes represent a focal point in a problem of coordination (Schelling, 1958).

All the above ideas will be considered in order to put forward hypotheses concerning thebehaviour of the agents participating in “Sum 10” experiments.

3. Method: the “Sum 10” experiment

3.1. Presentation of the experiment

Teams of three players are anonymously and randomly formed from participants to play agame of 36 rounds. See Appendix C for the instructions distributed to the participants. Each ofthe players has a set of numbers. This set remains unchanged in every round and is composed ofthe values 0, 1, 3, 4, and 10. In every round each player has to declare one of the numbers in thisset. The numbers of the three people playing together are then summed. Based on the sum, eachplayer receives a payoff, following the rules below:

∗if S(i) = 10, I(i) = 40 − D(i)

∗if S(i) > 10, I(i) = 30 − D(i)

∗if S(i) < 10, I(i) = 0 − D(i)

where S(i) denotes the sum of the team, of which player I is a member; I(i), player i’s individualpayoff; and D(i), the number declared by player i.

The game is divided into two parts. In the first part (rounds 1–26) the players are grouped withartificial agents. In the second part, the groups consist of a permanent group of human beings.Players do not know that they are playing with artificial agents. They are told that they will begrouped with two players in the first part, and with two new players in the second. They do notknow the number of rounds.


The way artificial agents play the game varies in three types of experiments (or groups) asfollows:

(1) Group one: one agent always plays “3”, and the other agent starts to play “3” (first choice)and repeats this number if in the preceding round the human player chooses “4”; otherwise,it plays “0”. Thus, in order to obtain a sum equal to 10, the human player should declare “4”.

(2) Group two: one agent always plays “4”, and the other agent starts to play “3” (first choice)and repeats this number if in the preceding round the human player chooses “3”;otherwise,it chooses “10”. This way, the human player should choose “3” in order to get the sum of 10.

(3) Group three: both artificial agents always choose “0” (in round one only, for technical reason,they play a different number; either “3” or “4”). Therefore, in order to obtain a sum equal to10 the players should play “10”.

The appendix presents the detailed instruction received by the participants and the computerscreen. In each round the players are asked to choose the number, and state (with a number from0 to 10) their satisfaction for the result obtained in the preceding round.

The experiment was carried out in November 2002 at the Centro Alex of the Universita delPiemonte Orientale in Alessandria, managed by the Centre for Cognitive Economics, by means ofthe software Swiee (Boero, 2001). Twenty-four first-year law students, attending an introductorycourse on economics, participated in this game. On the basis of the score obtained they weregranted credits for one of the four parts of the exam (they could raise their grade up to 10%,according to a rate of conversion that were not specified to stimulate each individuals to get thehigher payoff as possible).

A note on terminology is called for here. Groups and treatments are used synonymously. Thenumber chosen by the players is labelled as declared, played or choices. The first part of theexperiment is sometimes called “training period”. “Section” is used as synonymous of “part” (ofthe experiment), and “game” of “experiment”. The number between inverted commas indicatesa choice.

3.2. Aim of the experiment and preliminary hypotheses

As noted by Novarese (2003a), the strategy performed by a player in “Sum 10” depends onmany factors, which are related to both individual characteristics and the interaction with the othersduring the game. One of the main purposes of the present paper is examining possible effects ofthe first 26 rounds on players’ behaviour in the following part of the game. In this perspective, thefirst part represents a kind of training period (even though such an expression was never used inthe presence of the participants), which differs in each treatment not only because of the fairnessof the partners faced and the strategy used in order to get a positive score, but also in relation to theway how different players react to the same conditions according to their individual behaviouraltraits.

Therefore, based on the previous analysis and the findings of the pilot’s test for this experiment,the following three hypotheses can be proposed:

(1) The reaction to the artificial agents, faced in the first part, will be different among agents,especially in the first and third treatments. Some of the participants could fight the opportunismof their partners by playing low numbers as a reaction.


(2) As individuals manifest a tendency to shape their behaviour according to their experiences,different behaviour among players trained in the various treatments should be expected in thesecond part of the game.

(3) A person getting a high score (or, more precisely, high satisfaction) in the first part,thanks to a given strategy, should maintain it also in the following rounds, accordingto a reinforcement mechanism, even if in the new situation it proves to be no longerefficient.

4. Results

4.1. The first part of the experiment

Table 1 proposes the mean values of a series of variables in the first part of the game, so as tocompare the behaviour of the players in each of the treatments. Two statistical tests were carriedout to find out possible differences among them: the analysis of variance and the Kruskal–Wallistest for the Wilcoxon Rank Sums non-parametric analysis; they allow similar conclusions in allcases.

The main results are the following:

- The mean individual total score differs significantly among the treatments. The second one hasthe highest score, as expected. The lowest score is, surprisingly, that of group one.

- The percentage of “4” in treatment one is lower than those of “3” and “10” in treatment two andthree, respectively (these are the numbers necessary to reach sum 10 in each group, accordingto the strategy performed by the artificial agents).

- Group one has the highest mean number of “0”, and obtains the highest mean number of sumslower than 10, but has a lower mean number of “Sum 10”.

- Treatments are not homogeneous with regard to the mean differences between each player’sscores and the scores of the other players in the same team (this difference is expressed by thevariable disp1, which assumes a positive value when the subject gains a higher score than the

Table 1The results of the first part of the experiment by treatment

tr1 tr2 tr3 p-value t-test p-valueKruskal–Wallis

Mean of total score 205.5 854.6 407.7 0.00 0.00Mean number of rounds in which S(i) = 10 3.2 20 13.2 0.00 0.00Mean number of rounds in which S(i) > 10 5.5 3.9 0.0 0.00 0.03Mean number of rounds in which S(i) < 10 17.7 2.3 12.3 0.00 0.00Mean number of rounds in which players chose “0” 11.0 0.9 9.0 0.01 0.01Mean number of rounds in which players chose “1” 1.9 2.4 1.1 0.62Mean number of rounds in which players chose “3” 2.3 22.0 1.4 0.00 0.00Mean number of rounds in which players chose “4” 6.3 1.8 2.3 0.45 0.14Mean number of rounds in which players chose “10” 5.5 0.0 13.3 0.00 0.00Mean of disp1 −1.4 0.78 −5.1 0.00 0.00max1 16.8 22.4 16.0 0.01 0.05varmax 40.5 82.5 34.8 0.00 0.03

A bold type indicates that the value is significant at a level of the 10%.


others in the same team. A value of disp1equal to zero means that the score is equal among allmembers, whereas a negative value means that the subject gets a lower score).1

While a lower score and stronger opposition to the artificial agents’ strategy were expected inthe third treatment, players in group one, on the contrary, manifested the lowest level of adaptationto the environment and the worst performance. How can we explain this result? The experimentrequires both the players’ capacity to cooperate and collaborate. Coordination is easier in treatmentthree than in one, for the artificial agents in the former treatment always choose the same numbers.In the first treatment, on the contrary, one artificial agent changes its behaviour according to thenumber declared by the human player in the previous round. Therefore, it is more difficult tounderstand which is the best choice. This is also true for treatment two, in which the second agentin response to the sum in the previous round being lower than 10 plays “10”, thereby, resultingin a minimal score. The lower score and percentage of sums equal to 10 in treatment one is thenprobably also related to coordination problems, as it is difficult to imagine that players accept toplay “10” but not “4”.

The difficulties of coordination are confirmed by the result that treatment one has the higherpercentage of sums higher than 10 (showing that individuals do not refuse to choose a high number,but rather that they are not able to coordinate). Thus, in this game, choosing “0” is probably aself-protecting behaviour (“As I’m not able to make a positive score, instead I save points bydeclaring 0”) or a way to punish partners for not being clear in their strategies and not a way tocontrast the opportunism of the partners who try to impose a higher cost.

An important dimension of individual behaviour in this game, that is both a cause and an effectof the performance, is the stability of the choices, i.e., the fact that a player chooses the samenumber several times. When a team reaches a successful routine and maintains it, the choicesof its members are obviously stable. Yet, in this situation players may decide to change theirchoices for different reasons (see Novarese (2003a), who explored other versions of “Sum 10”using interviews with the players):

(a) They may desire to gain a higher score (or to increase their relative score with respect to thatof the other members).

(b) They may try to be fair towards the others and therefore change their choice.(c) They may change their choice just for a desire to change.

Before the equilibrium is reached, the stability of the choices indicates the strategy used bythe players, who can try to adapt their choice to the numbers declared by the others (or the choicemay be based on how they played in the preceding rounds) or impose their own preferences (inthis case, they may choose the same number for many rounds).

The attitude under examination can be analysed by means of different indicators. The firstappendix discusses them and explains why the attention is focused on max1 (“1” indicates thatthe index is computed on the first part of the experiment), defined as the frequency of the mostdeclared number. For example, if in the first part, a player chooses “0” once, “2” twice, “3” 15times, “4” and “10” four times, max1 will be equal to 15.

1 Human players in treatment three can make points only with negative values of disp1 and the variable can be equal tozero only if a player always declares “0”; for treatment one the situation is similar, but human players can reach a positivevalue by always playing “0”; for the last group the index can assume positive, null, or negative values.


Table 2Mean value of some indicators in the second part of the experiment by treatment

Treatment 1 Treatment 2 Treatment 3 p-value F-testANOVA

p-valueKruskal–Wallis test

Mean number of 0 declared 3 1.6 2.6 0.69 0.48Mean number of 3 declared 1.5 4.3 0.3 0.01 0.02Mean number of 4 declared 6.4 1.8 2.3 0.14 0.76Mean number of 10 declared 0.9 0.9 2.4 0.32 0.39

A bold type indicates that the value is significant at a level of the 10%.

Given the previous findings, group two obviously has the highest value of this index.

4.2. The second part of the experiment

In the second part, teams are entirely composed of human agents. Therefore, the performanceof the players is strongly dependent on that of their partners. The score is highly correlatedamong the members of each team (even when there is a negative correlation within the group).As a consequence, it is almost impossible (at least with relatively few observations) to evaluatethe differences in the performances of the subjects in different treatments. Also the analysis ofindividual behaviour, in term of numbers played and stability of the choices, is more difficult, andit is better to study the two aspects separately2.

4.2.1. Number declared in the second partIn the training period, players in treatments one and two were expected to declare a number

higher than “0”, whereas those in treatment three were expected to declare “10” repeatedly. Theresult of the training period found in the second group a higher frequency of “3”. In the secondpart of the game, interestingly enough, the same result emerged as well.

As indicated in Table 2, the subjects trained in group two continue to declare “3” more fre-quently than the others in the second part. Yet, when we try to test the hypothesis concerningthe differences in the frequency of the choices, we encounter the problem mentioned above: thenumbers declared by the players of the same team are interdependent with one another. Even ifthe training has some impact, the choice will be still determined also by the behaviour of thepartners. For example, when a team reaches a stable successful routine, an individual may alwaysplay “4” because the others propose a sum equal to six. However, before a routine is established,a person could play, say, “0”, because the sum of the partners’ numbers is lower than a givenamount.

This interdependence can be captured in the regression model by including an interdepen-dent/control variable that assumes a value equal to the absolute frequency of the rounds in whichthe sum declared by the other members of the team equal 10 minus “0”, “3”, “4” or “10”, respec-tively. For example, when the dependent variable is the number “3” played, the last regressor isthe frequency of cases in which the other partners declared a sum equal to seven. In addition to

2 The variable max is computed from the frequency with which the given numbers are declared, and so it is strictlyrelated to the choices. We cannot, yet, use only the latter indicator, because of the variety of possible choices and situations(for example: few players declared “3” many times; many players have a high value of max). It is, besides, interestingand useful to look for general tendencies that can go beyond the number chosen.


Table 3Estimations on the number of “x”, declared in the second part, controlling for the numbers declared by the other membersof the team

Dependent variable: numbers of x declared in the second part

x = 0 x = 3 x = 4 x = 10

Number of 10 declared in the second partby the other members of the team

0.74 (0.04) – – –


– 0.75 (0.00) – –


– – 1.05 (0.00) –


– – – 0.94 (0.00)

Dummy for training in treatment 1 1.11 (0.47) 0.50 (0.61) 0.39 (0.45) −0.55 (0.55)Dummy for training in treatment 2 0.29 (0.85) 2.03 (0.08) 0.43 (0.62) −0.79 (0.39)p-value F-test 0.15 0.00 0.00 0.00R2 0.23 0.62 0.75 0.48

“–” indicates a variable not included in the estimation; the value in parenthesis under the parameter estimates is the p-valueof the t-test.

that variable, the other regressors include two dummies for the treatments. Four OLS estimationsresults are presented in Table 3 for the four dependent variables including the numbers of “0”,“3”, “4” and “10” declared, respectively, in the second part.

Table B.1 in Appendix B presents a similar analysis with a different control variable: thenumber of “10” obtained by the team. This table shows that players in treatment two declare“3” almost twice often. It also shows that the subjects in the last treatment choose “10” a highernumber of times, for the coefficient associated with the first two treatments is negative.

The interdependence/control variable is significant in all four estimations (i.e., there is a higherchance that players declare “3” more often, for example, if their partners’ sum is equal to seven).Nevertheless, attention should be focused on the dummies that measure the impact of the training.Table 3 confirms the results of Table 2. Only the dummy for treatment two, in the estimationsof the numbers of “3” chosen, has a significant and positive value. Players from that set, in thesecond part, choose “3” more often, independently of the choice of their partners.

In the second group, during the training phase, choosing “3” is a good strategy for obtainingthe best score. In contrast, “0” is chosen as an emotional reaction and “10” is chosen as a rationalstrategy, which involves low satisfaction because of the unfair distribution of the payoff. Thiscould explain why only in one out of four cases is the same strategy of the first part maintained.Moreover, while all the players in group two chose “3” several times, not all the individuals inthe other treatments chose “0” or “10”. Therefore, it is difficult to detect a statistically relevanteffect among the groups, and a different kind of analysis is called for.

Table 4 shows the results of the estimation specified to explain the number of “0”s chosen in thesecond part, in relation to the frequency of the same choice in the first period and to the functioningof the team (this table, like the following ones, includes also estimations with the same variables,as a benchmark). This latter aspect is captured by the regressor that indicates the number of sumsequal to 10 obtained by the group. Such a variable is linked with the dependent variable in twoways: (1) as it is not possible to reach a sum equal to 10, individuals can decide to punish theothers or to protect themselves and (2) if the sum of the numbers declared by the partners is equalto 10, a person can, rationally, choose “0”. Thus, the model tests whether the frequencies of given


Table 4Estimation with the number of “0” declared in the second part as dependent variable, by treatment

tr1 tr3

Number of 0 declared inthe first part

– 0.25 (0.04) 0.29 (0.01) – 0.07 (0.79) 0.03 (0.90)

Number of sum = 10 inthe second part

−0.49 (0.36) – −0.67 (0.06) −0.40 (0.37) – −0.40 (0.44)

p-value F-test 0.36 0.44 0.02 0.37 0.01 0.69R2 0.14 0.52 0.77 0.13 0.79 0.14

“–” indicates a variable not included in the estimation; the value in parenthesis under the parameter estimates is the p-valueof the t-test.

numbers in the two parts are related, controlling for the effect of the interaction with the others.Treatment two is not included in this estimation, as almost nobody declared “0”. Other controlvariables have been tested, with the similar result (see Table B.2 in Appendix B).

The estimation results show significant differences between the two treatments. While nosignificant relationships can be found for the third treatment, for the first one, the number of“0” declared in the first part affects positively the choice of the same number in the second. Thepersistence of this choice can hardly be explained with the typical mechanism of reinforcementlearning, as in the first part it does not lead to a positive result (though it sometimes gives apositive satisfaction related to punishing partners’ free-riding, see Novarese and Rizzello, 2005).A possible hypothesis is that there is persistence in the perception of the environment, probablycaused by the emotions experienced (this will be explained later).

Table 5 shows the estimations for the number of “10” declared in the second part (see Table B.3in Appendix B for specifications with different control variables, leading to similar conclusions).The second group is again excluded as nobody chose “10” in the first part. In this case, for thefirst group of individuals there is a significant correlation between the number of “10”s played inthe two periods. For the third treatment there are no significant results.

The negative and significant sign of the variable related to the number of sum = 10, for treatmentone, implies that the team obtains such a result only if nobody chooses “0”. In other words, thehigher the frequency with which the team obtains a sum equal to 10, the less likely an individualwill choose “0” (sequences that are composed by two “0”s and one “10” are not observed). Incontrast, these equilibria are possible in the third treatment.

Table 6 presents the estimations for the number of “4”s. In this case the variable that accountsfor the team effect is the frequency of cases in which the sum of the choices of the partnersis equal to six (estimations with a different value are shown in Table B.4 in Appendix B; the


tr1 tr3


0.16 (0.01) – 0.16 (0.01) −0.19 (0.45) – −0.14 (0.59)

Number of sum = 10 inthe second part

– −0.11 (0.40) −0.11 (0.14) – −0.47 (0.25) −0.42 (0.33)

p-value F-test 0.01 0.40 0.02 0.45 0.25 0.47R2 0.67 0.12 0.80 0.10 0.22 0.26

See the notes to Table 4.


Table 6Estimation with the number of “4” in the second part declared as dependent variable, by treatment

tr1 tr2 tr3

Number of “4”declared inthe first part

0.16 (0.30) – 0.30 (0.00) 0.64 (0.04) – 0.05 (0.71) 1.01 (0.25) – 0.13 (0.50)

Number ofsum = 6 bythe partnersin the secondpart

– 0.81 (0.05) 1.12 (0.00) – 2.26 (0.00) 2.16 (0.00) – 1.06 (0.00) 1.03 (0.00)

p-value F-test 0.30 0.05 0.00 0.04 0.00 0.00 0.25 0.00 0.00R2 0.17 0.48 0.98 0.54 0.94 0.94 0.21 0.97 0.97


main conclusions are the same). Also in this case, the variable related to the first period is notsignificant for the third group, as well as for the second. Players chose “4” simply in response tothe behaviour of their partners. For the first treatment there is a positive link between the numberof “4”s declared in the two periods.

Table 7 shows the results of the estimations on the number of “3” (treatment three has notbeen included because only two players occasionally chose this number). The effect of the otherplayers’ choices is highlighted here by the variable number of “sum equal to seven” chosen bythe partners (see Table B.5 in Appendix B for another specification). For the second group, nocorrelation can be found between the two periods. Such result is not as strange as it might appear,since all the players of this treatment often chose “3” in the first part, and all of them had thetendency to choose it again in the second part (it seems that, if players repeat the choice beyond agiven level, the effect stabilizes). Nevertheless, only in some cases could they effectively continueto do so because of the partners’ behaviour. The most interesting result is related to treatmentone, where there is a correlation between the frequency of “4” in the first part and that of “3” inthe second, as if players were imitating the behaviour of the artificial agents faced in the trainingperiod.


tr1 tr2


0.06 (0.88) – 0.07 (0.87) – – 0.12 (0.62) – 0.12 (0.52) –


– – – 0.12 (0.07) 0.12 (0.10) – – – −0.04 (0.92)

Number ofsum = 7 bythe partnersin the secondpart

– 0 (1) 0.04 (0.94) – 0.05 (0.86) – 0.89 (0.03) 0.88 (0.04) 0.89 (0.05)

p-value F-test 0.62 1 0.99 0.07 0.22 0.88 0.03 0.09 0.12R2 0.04 0 0.01 0.45 0.45 0.00 0.58 0.61 0.58


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Table 8Estimation with max2 as dependent variable, all observations, by treatment

tr2 tr1 tr3

Number ofsum = 10 inthe secondpart

0.29(0.17)

0.25(0.16)

0.21(0.20)

0.26(0.18)

0.27(0.15)

0.23(0.19)

0.50(0.15)

0.48(0.21)

0.46(0.31)

0.63(0.06)

0.45(0.04)(0.02)

0.44(0.21)

0.72(0.00)

0.73(0.00)

0.75(0.00)

0.54(0.00)

0.71(0.00)

0.66(0.00)

Number ofsum = 10 inthe first part

– 0.13(0.09)

– – – – – −0.05(0.76)

– – – – – −0.04(0.70)

– – – –

disp1 – – – – −1.1(0.16)

– – – – 0.79(0.05)

– – – 0.21(0.45)

– – –

max1 – – 0.15(0.16)

– – – – 0.24(0.15)

– – – – – −0.48(0.11)

– –

Meansatisfaction inthe first part

– – 1.00(0.08)

– – – – −0.14(0.87)

– – – – – – 0.21(0.27)

Total score inthe first part

– – – – – 0.18(0.08)

– – – – – −0.11(0.34)

– – – – −0.04(0.66)

p-value F-test 0.17 0.10 0.08 0.14 0.14 0.08 0.15 0.37 0.38 0.13 0.05 0.24 0.00 0.29 0.01 0.06 0.28 0.01R2 0.29 0.60 0.64 0.54 0.54 0.64 0.31 0.32 0.31 0.56 0.70 0.44 0.78 0.78 0.80 0.87 0.79 0.82

Number of observation, 8.


4.2.2. Tendency to maintain a stable choiceThis section proposes a series of estimations to explain the value of the variable max2 in

relation to the individual strategy of the training period. The analysis is conducted by separatingthe treatments so as to detect possible differences.

Table 8 presents the results of a series of estimations. max2 is the dependent variable. Theregressors consist of several values that are proposed in the previous tables. Among them thereis also the mean individual satisfaction obtained in the first part. For general remarks on thisvariable, see Novarese and Rizzello (2005), which discusses the related methodological problemsand tests their validity.

The variable max2 is, again, not independent among the members of a team. The problem canbe solved by controlling the effect of the group on the variable measuring the number of “sumequal to 10” in the second period. If a team gets a sum equal to 10 for a given period, for thatset of rounds all of its members will have the same value of max2. In the estimation, this relationwill be highlighted by the control variable, so allowing the interdependence to be eliminated.Similarly, if a group is not able to coordinate, and players keep changing their choice, max2 willbe low, just like their number of “sum equal to 10”. The control variable will again account forthis interdependence. The results are discussed separately for each treatment, starting from thesecond one taken as a benchmark.

4.2.2.1. Treatments 2. The value of max2 is best explained by the variables related to the trainingperiod than by the number of “sum equal to 10” in the second. All the variables measuring theperformance in the first part (score, number of sum equal to 10, satisfaction, disp1, max1) areinterrelated and thus, have a similar effect individually on max2. The fit of the model is dominatedby two of them: the total score and the mean satisfaction (which have the same significance andthe value of R2).

How can this result be explained? Two possibilities are as follows:

(1) As it poses a relationship between the strategies employed in the two parts, it implies thatan individual player may maintain a repetitive behaviour during the game because of itssimplicity in dealing with uncertainty.

(2) An alternative explanation calls for a typical reinforcement effect, according to which thestrategy “repeating the same number” is more likely to be used by the players who discoveredits usefulness in the first part.

These two explanations are related: to get a higher score an individual should understand thatrepeating “3” permits the best results; this understanding can be achieved only by starting torepeat “3”. In the first part, to get a high score it is necessary to choose number “3” as many timesas possible in the following rounds. An indirect, but efficient (and general), way to measure thisobservation is using the total score, which is higher if the individual chose this number more timesin succession. If the score is high, the variable max1 should be high too, but max1 can also behigh if a player has repeated the same number but not in following rounds.3 In this case, the scorewill be lower, because of the reaction of the second artificial agent (who instead of playing “4”,

3 We cannot tell whether max2 is high because of the choices made in following rounds or not. Yet, it should be notedthat in the second period the total number of rounds is low, and then a high value of max2 requires necessarily that aplayer repeated a choice in following rounds: with 10 rounds, a value of max2 higher than six (obtained by six out ofeight individuals in this groups, while both the others obtained five) requires at least three following repetition of it.


will choose “10”). For this reason, the score is the best indicator of the way in which the first partwas played.

So, if the result found in Table 8 depends only on personal attitude, we would find a strongerlink between max1 and max2 than between max2 and the performance. Besides, the correlationbetween max in the first and second parts of the experiment is equal to 0.79. For the same group,the correlation (r = 0.97) between the number of “sum equal to 10” in the first part and max2 ishigher. The correlation between the number of 10 in the first half of the training and max in thelast round of it is 0.82, which again is higher than 0.79. The analysis of the satisfaction, presentedbelow, confirms this interpretation (for treatment one results are different).

In order to see if the performance in the first and second part of experiments are correlated,Table 10 presents simple correlation coefficients for the score and the number of “sum equal to10”, respectively, between the first and second part of experiments. Since none of the correlationcoefficients is significant, the results in Table 10 allow excluding a third possible explanation: therelationship under examination is not mediated by the correlation between the performance in thefirst and second part. So, we cannot simply say that some individuals are more adaptable or morecapable of playing this game, thereby obtaining a higher score in both the first and second part(and therefore getting a good score in the first and second part plus a related high number of 10).

It is important to observe that, not all individuals have “3” as a mode. In other words, someplayers used the strategy “repeat the same number” with different other choices, like “4” or “10”. Asuccessful training created a rigidity which goes beyond the tendency to repeat “3”. The repetitionof “0” could, for example, be a reaction to the difficulties faced with the new partners, given thehigh expectations created by the training.

4.2.2.2. Treatment 1. The mechanism found for the previous treatment does not work here. Infact, the level of max2 is now more affected by the number of “sum equal to 10” in the secondpart. The score in the first part has no significant effect. Nevertheless, there is a relation withindividual behaviour in the first part of the game. In fact, max2 is significantly affected by disp1,but the relation is now opposite to that of the previous treatment. Where disp1 is high (this meanspeople chose “0” many times in the training), max2 is high. In fact, in this case, their mean score(equal to about zero) is higher than that of the artificial agents (as one of them plays number “3”and gets a negative score as the sum result less than 10). Therefore, a person with a high disp1also has a low score and a high max1. These are the individuals seen in the Table 4 who choose“0” many times in the first part and continue to do so also in the second.

The estimations with the number of “sum equal to 10” in the first part have a worse fit thanthose without it, because in this set there are players who follow different models of behaviour:some of them learned the strategy of the artificial agents (and then play “4” or “3”), while othersrefused to or did not learn it.

4.2.2.3. Treatment 3. The variables related to the strategies in the first part are not relevant. max2is explained primarily by the behaviour of the team in the second part. max1 increases the fit ofthe estimation most among all regressors that are related to the first part. It has a negative sign(and a very low significance). In the first part, a high score of max1 is related to the use of thestrategy ‘play always “10”. In fact, the correlation between the number of “10” declared and max1is equal to 0.50, while the correlation between the number of 0 and max1 is equal to −0.60. Sucha strategy is not maintained in the second part (in fact, there is also a low correlation between thefrequencies of “10” in the two periods).


Table 9Estimation with max2 as dependent variable, on the sample of individuals who get at least one sum equal to 10 in the firstpart

tr2 1 tr2 2 tr2 3 tr2 4 tr3 1 tr3 2 tr3 3 tr3 4 tr1 and2/1

tr1 and2/2

Number of sum = 10in the second part

0.25 (0.17) 0.23 (0.19) 0.28 (0.16) 0.17 (0.30) 0.73 (0.00) 0.73 (0.01) 0.74 (0.00) 0.66 (0.00) 0.43 (0.01) 0.44 (0.05)

Number of sum = 10in the first part

0.13 (0.09) – – – −0.04 (0.70) – – – 0.12 (0.02) –

disp1 – – −1.1 (0.16) – – – 0.21 (0.45) – –sod101 (mean

satisfaction when asum equal to 10 isobtained in the firstpart)

– – – 0.92 (0.05) – – – 0.20 (0.30) – 0.08 (0.72)

Total score in the firstpart

– 0.18 (0.08) – – – −0.04 (0.66) – – – –

p-value F-test 0.10 0.08 0.14 0.06 0.02 0.02 0.02 0.01 0.01 0.12R2 0.60 0.64 0.54 0.68 0.78 0.78 0.80 0.82 0.65 0.37

Number of observation, 8 for the first eight columns and 12 for the last ones: (1) “–” indicates a variable not included inthe estimation and (2) the value in parenthesis under the parameter estimates is the p-value of the t-test; tr1 indicates theestimation performed on the first treatment, tr1 on the first and tr3 on the last, tr1 and tr2 on the first and second joined.

4.2.3. The impact of satisfaction on choiceTable 9 presents other specifications of the model, including the variable sod101: the mean

satisfaction of the rounds in which the individual gets a sum equal to 10 (the table also includessome of the estimations shown in Table 8, so as to simplify the comparison between the results).For treatment one there are only four individuals who got, at least once, a “sum equal to10” in the first part, and therefore the regression is not performed. Table 9 explains that thehigher the satisfaction individuals get from a “sum equal to 10” during the training, the higherthe probability that they have a high value of max2. This specification has the best fit of all(Table 10).

By using individual satisfaction as a measure of the reward (instead of the score, or of thenumber of “sum equal to 10”) we have, therefore, a better predictor of individual choice. Thisfinding is consistent with the idea that satisfaction plays a central role in determining behaviourand reinforcement effects. This result is partially true also for treatment three, where sod101 is themost significant variable among those related to the first part, and it is also the one that contributes

Table 10Correlation of the score and of the number of “sum equal to 10” in the first and second part, by treatments

All Treatment 1 Treatment 2 Treatment 3

Score in the firstpart − score in thesecond part

0.04 (0.86) −0.37 (0.36) 0.02 (0.95) 0.28 (0.50)

number of sum = 10 inthe firstpart − number ofsum = 10 in thesecond part

0.17 (0.41) −0.20 (0.62) 0.13 (0.75) 0.18 (0.67)

In parenthesis is reported the p-value of the Pearson’s test.


to a higher increase in the fit of the estimation (the specification tr3 4 has the higher valueof R2).

If we add the observations of treatment one to those of treatment two, sod101 has less capacityfor explaining the dependent variable and its significance. Some players of the first and the lastgroup express a high satisfaction when punishing their partners. Others express a high satisfactionin getting a good score or a “sum equal to 10.” This is probably the main reason for the low relevanceof such variable.

5. Discussion and conclusion

This paper proposed an exploratory experiment driven by some general hypotheses.

(1) The first hypothesis is that individual behaviour in experimental decision-making tasks isheterogeneous. The highest variability in the training is found when participants face oppor-tunistic partners and a difficult environment. Under such circumstances, some of them choosethe rational behaviour. Others behave in such a manner that seems to involve emotions, whichis consistent with other experimental findings. Specifically, findings from the comparisonbetween treatments one and three indicate two possibilities about how emotions affect thebehaviour. Some players are more willing to protect themselves from a behaviour difficult forthem to understand than to punish opportunistic partners, while others would rather acceptopportunism than an unclear interaction.

(2) The training significantly influences the way in which people play in the final part, confirmingthe second hypothesis about the effect of learning. Dissimilar trainings cause different resultsfor the behaviour in the final rounds. Since in the first part players in the same treatmentsbehave in different ways, their conduct in the second period is not expected to be identical.Thus, it is incorrect to compare groups as if they were composed of homogeneous agents. Thecurrent findings show that, given the treatment, the strategies of the second part are associatedwith the performance and choices made during the training. By taking heterogeneity of agentsinto account, the analysis becomes more difficult, but it is also more informative (Novarese,2003a).

(3) Given certain conditions of the environment (i.e., low degree of difficulty and fair partners) andcertain characteristics of the individuals, the findings of the current experiment confirm thoseof previous studies on the human tendency to replicate the choices that initially proved to besuccessful. This consideration offers new evidence concerning the reinforcement mechanismand the origin of the organizational “success trap” at the individual level (see Bonini andEgidi, 1999). The participants in some experiments tend to repeat the strategies they developinitially, even when they encounter changes in the conditions. Obviously, their choices arenot completely pre-determined, but the experience acquired beforehand does affect individual(and thereby team) performance.

As a consequence, team composition matters (as shown in Novarese, 2006, who alsoconfirmed the findings on individual learning by carrying out a similar experiment). Thenumber that any individual expects his/her partners to play is taken as the first step in themechanism of reciprocal adjustment. Ultimately, the process of team and individual learningbecomes strongly path-dependent, for it is affected by the way in which every person hasplayed in the first part and by the reciprocal interface.

Granted that, given certain conditions the relevance of mental routines in individualdecision-making is confirmed, we do not mean that agents always behave in a simple and


mechanical way. In fact, some players in the first treatment learned to imitate the strat-egy of the artificial agents with whom they played. Other players in the second groupdeveloped the strategy of “play always 3” in the first part, and then applied it to a dif-ferent number (for example, “play always 4”). Apparently, experiences can induce indi-viduals to form expectations concerning the choices of the other persons and they behaveaccordingly, even if the initial experiences are disconfirmed by reality. Usually, after somerounds, expectations should be updated. But in an interactive situation as the one pro-posed here, the initial choices can have a strong impact because of the reaction of thepartners.

There are other conditions that seem to stimulate players to reinforce behaviours, whichhave not proved successful. These conditions tend to involve emotions such as the needto protect themselves from a difficult environment and the unfairness of the partners).The emotions presented here are relevant to Rabin’s statement (1993, p. 1281): “thesame people who are altruistic to other people are also motivated to hurt those who hurtthem”.

Choosing “0” in treatment 1 can be seen as this type of reaction. A rational player, in fact,should play “4” and win 36. Even if the player did not understand the way the others agentsin the team were behaving, there would be another rational choice: playing “10”. In this case,the score would be 30, which is better than 0. So the decision to declare “0” seems to implythe desire to punish partners, even if this has a cost. In the last treatment, no strong learningeffects seem to emerge (both in terms of numbers played and of stability in behaviour). Thissuggests that some conditions may not induce persons to change their way of looking at theworld.

(4) A last element of novelty in this paper is related to the empirical analysis of the role ofsatisfaction in the process of mental routinization. Given the score, higher satisfaction ledto stronger rigidity in behaviour. No other experimental analysis is available in the literatureon the relation between satisfaction and decision. The current findings in this regard arepreliminary but very important in confirming the relevance of satisfaction to the developmentof routinized behaviours.

Acknowledgement

I thank Bijou Yang Lester for her comments and extended revision of the paper. I thank alsoAndreas Chai, Alexis V. Belianin, Louis Levy-Garboua, and Roger A. McCain (all participantsin the Conference “Cross-Fertilization Between Economics and Psychology”, SABE and IAREPjoint meeting, Philadelphia, July, 2004) for useful notes. This paper is a chapter of my PhD the-sis, discussed at the Idefi-Cnrs Universite de Nice Sophia Antipolis and supervised by ProfessorJean-Luc Gaffard. The experiment presented was carried out at the Alex Laboratory in Alessan-dria. I thank Guido Ortona and Marie Edith Bissey for their cooperation. The software used, inSwiee, was developed by Riccardo Boero. Other people participated in the management of theexperiment: Salvatore Rizzello, Paolo Parodi, Maria Teresa Servello, Alessandra Sterpone, andCesare Tibaldeschi. The English version was revised by Elena Pasquini.

Appendix A. Measuring the attitude to maintaining a stable behaviour

The attitude under examination can be analysed with different indicators. Table 1 presents twoof them. The first is the variable max1: the absolute frequency of the most frequently declared


numbers (if we took the relative frequency of the most frequent choice, the result would be thesame). The second index, varmax, is defined as the variance among the frequencies of the possibledifferent choices. If a player always chooses the same number, the varmax will assume the value116.6, as there would be one observation equal to 26 and four equal to zero. If a player choosesall the available numbers, with about the same frequencies, varmax value will be close to zero.Also this index indicates that in treatment two players tend to have more stable behaviours. Thisvariable has a different aspect, too.

While max1 focuses on the possible “equilibria”, varmax gives a more general view of thesearch strategy, i.e., of individual behaviour before reaching (when possible) a stable choice. It isthen interesting to look at its variance. It assumes the lowest value in treatment three (6.8 versus26.2 and 36.6) where there are the most homogeneous situations among players. Such differencesare highly significant according to Levene’s test (p-value equal to 0.005). Variable max1 indicatesthe same, but the differences are not statistically significant. In the first part of treatment three,almost all players declare both “0” and “10” (and also other numbers). Later they converge onone of these two alternatives. In the first treatment, some players converge quickly to one of thealternatives, while others do not. Therefore, there are more differences among players in thissearch process.

Appendix B. Other estimations to explain the number declared in the second part bythe players

See Tables B.1–B.5.

Table B.1Estimations on the number of “x”, declared in the second part, controlling for the numbers of 10 obtained by the team

Dependent variable: numbers of x declared in the second part

x = 0 x = 3 x = 4 x = 10

Number of sum = 10 −0.43 (0.06) 0.25 (0.16) 0.36 (0.14) −0.27 (0.10)Dummy for training in treatment 1 −0.99 (0.56) 2.05 (0.14) 1.24 (0.49) −2.30 (0.06)Dummy for training in treatment 2 −1.93 (0.24) 4.05 (0.00) −0.11 (0.95) −2.07 (0.07)p-value F-test 0.23 0.01 0.45 0.16R2 0.18 0.40 0.12 0.21


Table B.2Estimation with the number of “0” declared in the second part as dependent variable, by treatment

tr1 tr3

Number of 0 declared in the first part 0.28 (0.04) 0.22 (0.06) 0.29 (0.44) 0.13 (0.51)Number of sum = 0 in the second part

by the other players1.96 (0.14) −0.77 (0.39)

Number of sum = 10 in the secondpart by the other players

0.36 (0.66) 0.85 (0.05)

p-value F-test 0.10 0.05 0.65 0.12R2 0.60 0.70 0.16 0.57




tr1 tr3

Number of 10 declared in the firstpart

0.16 (0.03) 0.19 (0.01) 0.42 (0.11) 0.27 (0.56)

Number of sum = 0 in the second partby the other players

0.02 (0.96) 1.77 (0.01)

Number of sum = 10 in the secondpart by the other players

0.18 (0.30) −0.21 (0.45)

p-value F-test 0.06 0.03 0.03 0.64R2 0.67 0.74 0.75 0.16



tr1 tr2 tr3

Number of “4” declared in the first part 0.25 (0.01) 0.66 (0.04) 0.96 (0.25)Number of sum = 10 by the team in the second part 1.1 (0.00) −0.25 (0.32) 0.57 (0.24)p-value F-test 0.00 0.08 0.26R2 0.89 0.63 0.41



tr1 tr2 tr3


0.09 (0.81) 0.07 (0.70) 0.06 (0.53)


0.11 (0.11) −0.10 (0.80) 0.03 (0.53)

Number of sum = 10 inthe second part by theteam

−0.24 (0.34) −0.15 (0.42) 0.90 (0.06) 0.92 (0.05) −0.13 (0.00) −0.13 (0.00)

P-value F-test 0.60 0.15 0.13 0.14 0.02 0.01R2 0.18 0.52 0.55 0.54 0.81 0.81


Appendix C. Instructions for the experiments distributed to the participants

Game sum 10The game is divided into two parts. Each part is subdivided into a number of rounds.The computer randomly and anonymously groups three players.In each turn you have number 0, 2, 3, 4, 10 (included) at your disposal and you have to declare

one of them.Your number will be added to that of the two players in your group.On the basis of the sum obtained, the score will be determined by these rules, identical for the

three players:


- If the sum is 10, score = 40, the number declared; for example, if you declared 4, and both otherplayers in your group declared 3, the sum is 10; you gain a score of 40 − 4 = 36, the other twoplayers gain 40 − 3 = 37.

- If the sum is higher than 10, score = 30, declared number; for example, if you declared 4, thefirst player in your team declared 4, and the second declared 3, the sum is 11; your score is30 − 4 = 26; the second player gains 30 − 4 = 26, and the third one gains 30 − 3 = 27.

- If the sum is lower than 10, score = 0, declared number; for example, if you declared 4, the firstplayer in your team declared 0, and the second declared 3, the sum is 7; you gain 0 − 4 = −4(you lose 4); the second player gains 0 − 0 = 0; the third gains 0 − 3 = 0 (the player loses 3).

All through the first part you will be grouped with the same two players.In the second part (your computer will inform you when the second part starts) you will be

grouped with two other players, who will be the same until the end of the game.(This is the page you will see on your computer (Fig. 1)).At each round you will be asked to answer the following questions:

- On a scale of 0 (unsatisfied) to 10 (satisfied), what is your level of satisfaction for the result youobtained in the preceding round?

- What is the mean sum you expect to gain in the following rounds?

Fig. 1.


Before going on to the next round, it is necessary to wait until all players (not only the onesgrouped with you) have answered. You might have to wait. Be patient! The computer will passto the new page automatically, as soon as it is possible to continue.

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