supply chain information sharing in a macro prediction market

42 (2006) 1944–1958www.elsevier.com/locate/dss

Decision Support Systems

Supply chain information sharing in a macro prediction market

Zhiling Guo a,⁎, Fang Fang b, Andrew B. Whinston c

a Department of Information Systems, UMBC (University of Maryland, Baltimore County), Baltimore, MD 21250, USAb Department of High Tech Management, College of Business Administration, Cal State Univ — San Marcos, San Marcos, CA 92096, USA

c Department of Information, Risk, and Operations Management, McCombs School of Business,The University of Texas at Austin, Austin, TX 78712, USA

Received 4 April 2006; accepted 10 May 2006Available online 17 July 2006

Abstract

This paper aims to address supply chain partners' incentives for information sharing from an information systems designperspective. Specifically, we consider a supply chain characterized by N geographically distributed retailers who order ahomogeneous product from one manufacturer. Each retailer's demand risk consists of two parts: a systematic risk part that affectsall retailers and an idiosyncratic risk part that only has a local effect. We propose a macro prediction market to effectively elicit andaggregate useful information about systematic demand risk. We show that such information can be used to achieve accuratedemand forecast sharing and better channel coordination in the supply chain system. Our market-based framework extends therange of information sharing beyond the supply chain system. It also opens the door for other corporate risk managementopportunities to hedge against aggregate economic risk.© 2006 Elsevier B.V. All rights reserved.

Keywords: Supply chain; Information sharing; Macro prediction market; Rational expectations equilibrium

1. Introduction

Information asymmetry is a main source of systemsinefficiency in many areas. For example, the well-knownbullwhip effect [22,31] refers to the information distortionthat is caused by misaligned incentives to share privatedemand information truthfully among self-interested sup-ply chain partners, resulting in direct deadweight losses insocial welfare. Truthful information sharing has been pro-posed as a solution to the bullwhip effect. Over the past fewyears, new business initiatives enabled by emerging tech-

⁎ Corresponding author.E-mail addresses: [email protected] (Z. Guo), [email protected]

(F. Fang), [email protected] (A.B. Whinston).

0167-9236/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.dss.2006.05.003

nologies such as Electronic Data Interchange (EDI), RadioFrequency Identification (RFID), and XML-streamlinedworkflow management have facilitated information shar-ing in decentralized business environments. However, atechnologically effective system does not necessarily resultin improved decision quality unless it is economicallyefficient as well. Systems could still be inefficient if usersonly strategically report information for their own benefit.We seek to investigate the incentive issues for supply chaininformation sharing. In particular, we propose a market-based framework to understand how conflicting incentivescan be aligned and useful information can be elicited in thenew supply chain information systems design so that abroad scope of benefits can be achieved.

In this paper, we consider a simple two-echelon sup-ply chain characterized by N geographically distributed

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http://dx.doi.org/10.1016/j.dss.2006.05.003

1945Z. Guo et al. / Decision Support Systems 42 (2006) 1944–1958

retailers who order a homogeneous product from onemanufacturer. Each retailer serves her own consumermarket whose demand uncertainty can be expressed as thesum of two randomelements— amacro risk factor and anidiosyncratic risk factor. The macro factor represents thesystematic risks caused by uncertain macroeconomicevents that affect all retailers, such as an economic down-turn. The idiosyncratic factor represents local market risksunique to individual retailers, such as the effect of weatheron their localmarkets. Before a selling season each retailerreceives a noisy signal about the macro risk and orderinventory from themanufacturer based on the informationavailable to her. The manufacturer, who has no consumerdemand information, is interested in forecasting expectedaggregate orders from all retailers. The retailers, who bearthe uncertainty of the consumer markets, are interested ineffectively forecasting future demand. Our goal is to de-sign a new supply chain information system that alignsdifferent supply chain partners' self-interests and thus en-ables more effective information sharing and better deci-sion-making. Some critical questions must be answered inpursuit of this goal: What information could and should beshared? How do we effectively share this information?

In answer to the first question, we argue that the newinformation system should focus on forecasting element atan appropriate aggregation level. A too broad forecastinggoal may seem less relevant and a too narrow forecastinggoal may not attract sufficient attention, leading to a lesseffective prediction. In this supply chain context, we shouldfocus on the macro factor that will affect all the retailersinstead of extracting individual retailers' overall forecasts.There are several reasons. First, the manufacturer is mostinterested in the macro factor forecast since the idiosyn-cratic risks are independent. The total idiosyncratic effectsfrom all the retailers can be cancelled out by the Law ofLarge Numbers. Second, individual retailers are not inte-rested in sharing their idiosyncratic factor forecasts becausethey have the best knowledge and are not concerned withthe local risk of others. They are, however, interested inmacro factor forecast because it affects the forecast accu-racy of their own demand. This common interest among allsupply chain partners can guarantee market liquidity andensure that no individual's private interests can signifi-cantly mislead the aggregate opinion. Manipulation of in-formation can be potentially reduced. Therefore, a marketdesigned to forecast the macro factor (i.e., a macro pre-diction market) is a viable candidate mechanism to elicitand share dispersed information.

As to the mechanism for effective information sharing,using a prediction market to elicit information is an emer-ging research field. A prototype example is the IowaElectronic Market (IEM: http://www.biz.uiowa.edu/iem/)

that predicts presidential election outcomes. Other exam-ples include the Hollywood Stock Exchange Market(http://www.hsx.com), primarily used to predict enter-tainment events such asmovie sales, and Goldman Sachs'Economic Derivatives Market (http://www.gs.com/econ-derivs/), inwhich likely outcomes of future economic datareleases (such as retail sales or industry production) aretraded. In our context, the macro prediction market isdesigned as a real money futures market, in which a retailindex with a payoff dependent on the future realization ofthe macro factor is traded.

The macro prediction market has many benefits. First,themarket offers a goodmechanism to effectively combinebeliefs in producing a reliable forecast. Market participantswith heterogeneous beliefs express their opinions about theretail index through their trading behaviors. Since traderswho make better predictions can expect higher payoffs, theprediction market can effectively attract whoever havegood information and aggregate it. Second, the marketaligns traders' incentives to trade because no individual ispivotal in influencing market price. Once the number ofparticipants is large enough, one retailer's nonparticipationor misrepresentation of information decreases only thatretailer's own profitability. It affects neither market pricenor the accuracy of market prediction conveyed in theprice. Therefore, the retailer's dominant strategy is to tradeaccording to true information. Third, the market is an opensystem that absorbs useful information from sources out-side the supply chain system. Speculators, liquidity tradersand others can participate as long as they believe they haverelevant information. This increases market liquidity andimproves forecast effectiveness as the number of marketparticipants increases. Finally, using futures markets inmacro variables affecting the economy to hedge currentlyunhedgeable risks is amarket innovation advocated byRef.[29]. Our idea of a macro prediction market opens the doorfor new opportunities in corporate risk management.

In this paper, we develop a model that shows that theinformation incorporated into the macro prediction mar-ket price is accurate enough to reduce the supply chain'stotal forecast uncertainty. The information also reducesthe retailer's order variance, which can significantly alle-viate the bullwhip effect. We demonstrate that demandforecast sharing and channel coordination can be collec-tively achieved in the macro prediction market-basedsupply chain information system. Expected supply chainefficiency is improved under market coordination.

To the best of our knowledge, this research is the firstto incorporate a prediction market in a supply chain con-tractual context. Since our focus is the informational con-tent of creating newmarket on supply chain efficiency, welimit our investigation of the contract format to the widely

http://www.biz.uiowa.edu/iem/

http://www.hsx.com

http://www.gs.com/econderivs/

http://www.gs.com/econderivs/

1946 Z. Guo et al. / Decision Support Systems 42 (2006) 1944–1958

used price-only contract, i.e., the manufacturer sets a unitwholesale price and leaves the order quantity decisions tothe retailers. Other complicated contract forms such asreorder/buy back contracts, non-linear pricing/quantitydiscount policy, and linear transfer payments are possible.We choose the simple contract form in order to generateand present some clean analytical insights.

This paper is organized as follows. We review relatedliterature in Section 2. In Section 3, we present our basemodel under a supply chain information sharing frame-work. We analyze the manufacturer's and retailers' deci-sion problems and discuss the construction of a macroprediction market. We further explore the value of infor-mation sharing and properties such as order variances andsupply chain efficiency in Section 4. We extend the mar-ket's role of information aggregation to risk hedging inSection 5. We conclude in Section 6 with an agenda forfuture research.

2. Related literature

The value of information sharing has been widely stu-died in the supply chain literature (e.g., [8,9,24]). Onesolution to alleviate the bullwhip effect was centralizingdemand information from supply chain partners [10].However, information sharing across the supply chain isnot easily achievable. In general, there is a conflict of in-centives in supply chain systems; individuals manipulateinformation solely for their own benefit. An effective in-formation system should be able to align incentives fromusers with conflicting objectives. Incentive alignment be-comes an important third dimension (preceded by softwareengineering and user acceptance perspectives) for any so-phisticated information systems design and evolution [2].

In this paper, following the finance literature, werepresent retailers' demand uncertainty in two parts: sys-tematic risk and idiosyncratic risk. Idiosyncratic risk sha-ring has attracted considerable attention in the supply chainfield. For example, Risk pooling in inventory and alloca-tion decisions by retailers facing local stochastic demandswas considered in Ref. [1]. The impact of a secondarymarket was examined by Ref. [23] where retailers (“re-sellers” in their paper) can trade their excess inventoriesassociated with independent demand risks among eachother. Since systematic risk cannot be reduced by riskpooling, it was suggested to use macro economy relatedmarket instruments to hedge certain aggregate economicrisks [29]. This paper complements previous work by in-vestigating the role of information aggregation in dealingwith systematic risk.

Economic theory has long recognized that a properlydesigned market efficiently collects and disseminates in-

formation [16]. New market efficiency research suggeststhat information markets can effectively aggregate infor-mation and produce advance forecasts of uncertain out-comes. An informationmarket is primarily designed for thepurpose of eliciting a particular piece of information. It is anemerging form of financial markets in which the settlingcontracts are futures contracts. It is also called “ideasfutures”, “event futures”, “Internet-based virtual stockmar-ket”, etc. A survey on research in information markets wasgiven by Ref. [34]. It was further suggested that informa-tion market-based forecast could be used for effective de-cision support [4]. Empirical study also showed evidencethat Internet-based virtual stock market forecasts out-perform alternative methods such as surveys and opinionpolls [30]. It was proposed that organizing Internet-basedinteractions to better gather predictive information. Wecomplement previous work by theoretically justifying thereliability of the market prediction mechanism. Moreover,we integrate the prediction function into the decision sup-port and theoretically validate both market performanceand efficiency improvement in the supply chain application.

Rational Expectations Equilibrium (REE; see e.g. Refs.[26,14]) is the theoretical support for the informationrevelation and aggregation in market transactions. The keyto the REE concept is that the act of trading conveys in-formation. The learning in the market is solved via anapplication of Bayesian rule [27]. This research shows howthe market can provide an incentive to effectively aggre-gate and reveal private information and howmarket price isa sufficient statistic for predicting the demandmacro factor.The concept of REE has been applied to supply chains tostudy the informational role of an industrial exchange (seeRefs. [25,33]). Previous work viewed spot market tradingas an opportunity to readjust inventory positions and shareinformation about demand uncertainty. In contrast, wepropose a futures market trading a financial index whosefuture payoff depends on realization of the macro factor. Inour futures market, demand uncertainty information can berevealed early and incorporated into the supply chain part-ners' decisionmaking. Ourmarket has two other importantadvantages. First, the trading information indices ratherthan the physical commodities can reduce transaction costsand so improve market liquidity. Second, our predictionmarket allows outside traders to present their relevantknowledge, extending the range of information sharing.

Our modeling framework is distinct from all previouswork in information economics. By dividing demand un-certainty into a systematicmacro factor and an idiosyncraticlocal factor, we propose trading a retail index representingsystematic risk in the supply chain in a macro predictionmarket, which has strong resemblance to a financial mar-ket. This idea is consistent with the findings that a firm's


demand has a strong correlation with some financial index[13]. A number of details about the construction of newmarkets and a variety of new products to deal with macroeconomic uncertainty from a risk hedging perspective wereprovided by Ref. [29]. In contrast, we focus on the in-formational role of markets and extend its function to riskhedging in the supply chain information system.

We study a supply chain in the framework of news-vendor problem. The traditional newsvendor model onlytakes into account a single decision maker's order quantitydecisionwhen facing exogenous demand distribution [18].Strategic interactions between a manufacturer and a re-tailer were studied by Ref. [21]. Their model allowed themanufacturer to change the wholesale price and the uncer-tain demand distribution can be updated through forecas-ting.We extend the demand forecast tomultiple retailers ina market framework. In terms of market setup, our modelis comparable with the work in Refs. [19] and [20] inwhich the information was revealed through the trading ofa financial asset. As to the market structure, we bothassume that orders are batched together to transact at asingle regret-free, market-clearing price.

3. The model

Consider N geographically distributed retailers whoorder a homogeneous product from a manufacturer. Eachretailer faces uncertain market demand, composed of sys-tematic risks that affect all the markets and idiosyncraticrisks that affect only the local market. We express theretailer i's demand as Di=ai+biθ+εi, i=1,…, N, wherehfN l; 1s

� �1 is a systematic macro economic factor andeifNð0; 1

seÞ is an i.i.d. idiosyncratic random factor. We

assume that ai and bi are known constants that could differamong different retailers but these are common knowledgein the supply chain.

We assume that each retailer can privately derive aforecast (or obtain a private signal) θi for the macroeconomic factor θ. Denote θi=θ+δi, where difN 0; 1

sd

� �is also i.i.d., indicating the forecast error. We also assumethat τδ>τ. This condition implies that the forecast is in-formative because the forecast variance is less than thevariance of the prior distribution of the macro factor.

Suppose the private information from individual re-tailers can be aggregated and define the aggregate signal as

1 Using the reciprocal of precision τ to denote variance is a standardtechnique in statistics and information economics. We use N to denotethe normal distribution when referring to a distribution, and use Φ andϕ to represent the standard normal cumulative distribution functionand the density function, respectively.

h u 1N

PN

i¼1hi ¼ hþ 1

N

X N

i¼1di, which is a sufficient statistic

for the full information reflected in a set of signalrealizations (θ1,θ2,…, θN). θ is the best predictor comparedwith any individual forecast since it has the same meanbut the least variance. We call this case truthful forecastsharing. Corresponding to this scenario is the aggregateinformation supply chain structure (Structure A). Thisprovides us with a full information benchmark solutionto whichwe compare two other supply chain structures: afully decentralized one (Structure D) and a macroprediction market-coordinated one (Structure M).

The supply chain partners' decision problems are thesame under all three supply chain structures. The manu-facturer sets a wholesale price to maximize the expectedprofit based on the expected aggregate retailer order quan-tity. Given the manufacturer's wholesale price, each re-tailer decides on an optimal order quantity based on herdemand distribution forecast. The only difference amongthe three structures is the information incorporated in fore-casting the demand distribution. In the truthful forecastsharing scenario (Structure A), the manufacturer has ac-cess to all the information. In the fully decentralized sce-nario (Structure D), the manufacturer cannot observe anyof the retailers' forecasts. From a social welfare perspec-tive, full information sharingwill generate higher expectedsupply chain profits. However, because higher individualretailer's profit is not guaranteed, it is not clear if a retailerwill want to truthfully share information. To achieve thegoal of information sharing, we design a macro predictionmarket-coordinated supply chain structure (Structure M)to trade a retail index. The retail index is an aggregateeconomic measure for the macro factor θ. For simplicity,we assume that the retail index payoff is exactly θ, de-pending on the future realized value of the macro factor.The index market price is a public signal that the manu-facturer and retailers use to update their beliefs aboutdemand distribution. We call this market-based forecastsharing. In this case, each retailer can gather informationfrom a public signal and a private one. The retailer decideshow much to rely on the public signal based on its pre-cision. We will compare the supply chain performanceunder the two types of forecast sharing (Structures A andM). In addition, we characterize conditions under whichthe market-based forecast sharing will outperform the fullinformation benchmark thus additional benefits can begenerated in the supply chain.

In the following, we present a macro prediction marketmodel and characterize its equilibrium and properties underthe REE framework. We then use backward induction tosolve the supply chain decision making problems underStructures A, D, and M. First, we derive the individualretailer's order decision in the supply chain as a best

3 Without confusion here we use the same notation i to denote bothretailers and outside informed traders.4 Conjecture and prove the existence of a linear REE is a standard


response function to the manufacturer's wholesale price.Then we solve the manufacturer's optimal pricing problemaccording to the expected aggregate orders from theretailers. We also characterize how the level of informationsharing affects the supply chain partners' decision making.

3.1. The macro prediction market

The construction of the macro prediction market is animportant market mechanism design issue that evokesvarious discussions. For our purposes, the trading asset is afutures contract based on a retail index θ, whose payoffdepends on the future likely outcome of macro economicevents such as retail sales. For simplicity, we assume thatone share of the retail indexwill pay outmonetary units θ.2

The current price of the futures contract is denoted by p.We assume that the macro prediction market operates

like an open book call futures market (see [12] for a refe-rence). The market opens at a pre-specified time, beforewhich traders can update their orders according to theirnew information. Trades take place at an equilibrium pricereflecting traders' regret-free trading decisions. For thesake of liquidity, we assume that only the risky asset θ istraded at the initial running of the market. Aggregatemarket information is revealed after the settlement fortransaction of θ. At this point, nobody has an informationaladvantage to arbitrage the market. The market is completeand efficient under the REE. Once the index price is set,the index-based derivatives can be properly priced, andvarious index-based derivatives can be traded. Therefore,our macro prediction market allows for derivatives tradingwhich can be used for risk hedging purpose (we will dis-cuss this in Section 5). In the following, we derive themarket equilibriumwhere only one risky asset, θ, is traded.

The way of designing an effective pricing mechanismis not unique. In this paper, we focus on amarket structurewhere the market maker responds to the aggregate netorder by taking an opposite position. We assume that themarketmaker doesn't have any private information. Thus,to prevent economic loss, the market maker sets the indexprice as the expected value of the future payoff given thecurrent aggregate net orders in the market.

We assume that there areM risk neutral informed tradersin themarket.M=N+N0,whereN is thenumberof retailersand N0 is the number of outside traders who have relevantinformation.We don't distinguish among informed traders'forecast abilities, but this simplification will not affect our

2 Note that we use θ to refer to either the trading asset (the retailindex representing the macro factor) or its random payoff inter-changeably. Interpretation should take into account the context inwhich it is used.

results. We assume that each informed trader i obtains aprivate signal θi=θ+δi, where difN 0; 1sd

� �, and places an

order πi for i=1,…, M.3 There are also some uninformedtraders (also known as noise traders) whose aggregate netorder is random and exogenously given, i.e.XfN 0; 1

sX

� �.

Note that the noise traders' assumption incorporates all theunpredictable elements which may come from agents'random liquidation demands or irrational behaviors. Therandom supply provided by noise traders is crucial inproviding the informed traders with proper incentives toparticipate in the market. Informed retailers will earnpositive expected profits at the expense of the noise traders'expected losses in equilibrium.

The informed trader i takes the price information intoaccount and strategically orders πi to maximize herexpected return from the macro prediction market.

maxpi

E½ðh−pðyÞÞpij hi; p� ðIÞA REE equilibrium is defined by two components.

First, a trading strategy πi, for i=1,…, M, that solves theabove maximization problem given pricing function p(y). Second, a pricing function p(y) such that given thetrading strategy πi, i=1,…, M, we have

pðyÞ ¼ E hjy ¼XMi¼1

pi þ X

" #ðIIÞ

where y ¼PMi¼1 pi þ X is the aggregate demand. The

following propositions characterize the market equilib-rium properties.

Proposition 1. For any given number of informedtraders M, there exists a unique linear REE in which

1) An informed trader i adopts a linear trading strategyπi=β0+β1θi+β2p, where β0, β1, and β2 are constants;

2) The equilibriummarket price p ¼ A0 þ A1PM

i¼1 hi� þ X

LÞ,where A0, A1, and L are constants.4

From Proposition 1, we can see that the symmetriclinear trading strategy is revealing since an informed tra-der's private information θi is indirectly transformed intothe trader's market trading volume πi based on anyobserved market price p. In turn, observing the index price

technique in financial economics literature. Although structurally similarresults are obtained, we are not simply reproducing it since our informa-tional assumption is different from other available results.We admit that byfocusing on the existence and uniqueness of a linear REE, we do notexclude the possibility of other non-linear REEs, which is not a generalinterest for researchers.

5 The Normal Learning Theorem gives the following rule for belief

updates: let the prior distribution hfN l;1

s

� �, and let θ=θ+ ε, where

efN 01se

� �and independent of θ. Then, if θi is a realization of θ, the

posterior distribution hj h i fNs

sþ selþ se

sþ seh i;

1

sþ se

� �.


p is equivalent to observing the signalPM

i¼1 hi þ XL

� �, which is

an indicator of the available aggregate market information.It's worth mentioning that under the notion of REE, tradersstrategically reveal and manipulate their private informa-tion, although such behavior proves to be self-revealing.

The existence of linear REE guarantees that p is alsonormally distributed. This fact allows us to characterizethe supply chain partners' belief updates using the NormalLearning Theorem (actually a standard Bayesian updateformula for normal distribution used in financial markettrading, see Ref. [27]). The uniqueness of the linear REEguarantees one-to-onemapping from the dispersedmarketsignals to the aggregate market price. L, which often re-presents market liquidity in the REE literature, reflects theprecision of the information transformation. The larger thevalue of L, the less the influence of X . Therefore, p is amore precise indicator of the useful signals.

The accuracy of aggregate forecasts revealed by themarket price can be increased when the number of in-formed traders increases.We define price informativenessas PIu

1Var½hjp�. The uncertainty on θ should be reduced

based on a good prediction p. In other words, the lessvariation of θ conditional on p, the more informative theindex price p is. We use the reciprocal to capture thisrelationship in the definition.

Proposition 2. Price informativeness PI increases inM. limMYl PI ¼ l and limMYl p ¼ h.

Price precision is a function of the number of informedtraders. Proposition 2 implies that when the number ofinformed traders approaches infinity, the information re-vealed in the macro prediction market will be accurateenough so that the index price converges to the true valueof the macro factor.

It's worth noting that one retailer's macro predictionmarket order will have negligible effect on the informationcontained in the index price because the equilibriumprice isdetermined by the sum of informed and uninformed tra-ders' signals. No individual's order is pivotal. In the macroprediction market, retailers can increase profit by solelytaking advantage of their superior private information. Theydo not profit by manipulating their trading orders hoping tomislead the manufacturer in her supply chain pricing deci-sion. Therefore, retailers' macro prediction market decisionsand physical supply chain order decisions are perfectly se-parable. In the following, we study the retailer's decisionproblem under different supply chain structures.

3.2. The retailer's decision problem

Suppose all retailers charge a fixed retail price r in theconsumer market. In this paper, we assume the retail price

is exogenously given and cannot be influenced by eitherthe retailer or the manufacturer. While strategic price de-termination either from the manufacturer or the retailers'point of view is an interesting research topic, it is not ourfocus here. Introducing too much heterogeneity such asdifferent prices in different markets or toomuch flexibilitysuch as pricing decision in the consumer market will dra-matically complicate our analysis without further incre-mental value in deriving our main insights.

In the following, we compare retailers' decision prob-lems under three supply chain structures A, D, and M.Weuse superscript a, d and m to distinguish parameters in thethree supply chain structures A, D, and M.

Given the wholesale price sj, for j=a,d,m, the retailerchooses an order quantity Qi

j, for j=a,d,m, to maximizethe expected profit according to the different informationat each setting. The retailer's decision problem is (RA)(RD) and (RM).

maxQa

i z0E½rmin½Qa

i ;Di�−saQai j h � ðRAÞ

maxQd

i z0E½rmin½Qd

i ;Di�−sdQdi j hi˜ � ðRDÞ

maxQm

i z0E½rmin½Qm

i ;Di�−smQmi j h˜i; p� ðRMÞ

where min [Qij,Di], for j=a,d,m, is retailer i's sale in the

consumer market. These standard newsvendor problemshave different demand distribution functions representingthe retailer's uncertainty about future demand under dif-ferent information and supply chain structures. Theoptimal order quantity is offered by the newsvendor so-lution; we only need to characterize the respective dis-tribution functions. The demand cumulative distributionfunction is normal by construction in (RA) and (RD). In(RM), with the linear price function we derived in Pro-position 1, the retailer's updated belief, based on theprivate signal and public price, will remain normal. Wecan apply the Normal Learning Theorem5 (see [27] for areference) to derive the analytical expressions for thedistribution functions under Structures A, D, and M.

Lemma 1. Define sv ¼ M−1sd

þ 1L2sX

� �−1and h−i u

Pjpi hj.

Retailer i's optimal order quantity is determined by

Q ji ¼ ai þ bil

ji þ

1ffiffiffiffiffis ji

q U−1 1−s j

r

� �; for j ¼ a; d;m


where

lai ¼s

Nsd þ slþ Nsd

Nsd þ sh ;

ldi ¼s

sþ sdlþ sd

sþ sdhi;

lmi ¼ sl

sþ sd þ ðM−1Þ2svþ sd hisþ sd þ ðM−1Þ2sv

þ ðM−1Þsvsþ sd þ ðM−1Þ2sv

h−i þ XL

� �

1sai

¼ b2isþ Nsd

þ 1se;1

sdi¼ b2i

sþ sdþ 1se;

1smi

¼ b2isþ sd þ ðM−1Þ2sv

þ 1se:

Lemma 2. limMYl EXlmi ¼ limNYl lai , and limMYl

smi ¼ limNYl sai .

Lemma 3. If N < 1þ M−1

1þ 2 1þM sdsð ÞMffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ð5M 2−4Þþð4M−2ÞM 2sdsþM2sd2

s2

q−M 1þsd

sð Þ

;

then smi > sai :

Lemma 2 implies that when both the number of informedmarket participants and the number of retailers approachinfinity, the macro prediction market yields a forecast asaccurate as the aggregate forecast in terms of the meanand variance of the forecasted demand distribution.Lemma 3 gives a condition under which the retailer'sdemand prediction is more precise using the macroprediction market than aggregate information sharing.Loosely speaking, given N retailers, the more preciseeach retailer's information (represented by τδ /τ), themore informed market participants are needed before themacro prediction market forecast will outperform theaggregate forecast. In addition, given the precision levelof each retailer's information, the more retailers in thesupply chain, the more informed market participants areneeded before the macro prediction market forecastoutperforms the aggregate forecast. This condition iseasy to be satisfied. For example, given τ=1, τδ=2, ifN=4, then M=35; if N=6, then M=77; and if N=20,thenM=819. But given τ=1, τδ=4, ifN=4, thenM=59;if N=6, then M=137; and if N=20, then M=1579.

Lemma 3 has important implications in the supplychain information systems design. In the absence ofgood incentives, truthful information sharing amongretailers is problematic. In contrast, our proposed macro

prediction market automatically aligns the retailers'incentives to reveal their private information. Further-more, the macro market-coordinated information shar-ing can absorb useful information from other marketparticipants. It has the potential to achieve more accurateforecast than what is available under truthful informa-tion sharing among retailers.

However, forecast accuracy alone cannot determineretailer profits because the manufacturer can use thesame information to make pricing decisions.

3.3. The manufacturer's decision problem

The manufacturer wants to choose the most profitablewholesale price s j, for j=a,d,m, based on the expectedaggregate order from the retailers. We assume that thereis no fixed cost and that unit production cost is a constant,c. We also assume the manufacturer will produce anamount equal to her expected orders from retailers. Themanufacturer's decision problems under the three supplychain structures can be expressed as follows:

maxsaz0

ðsa−cÞXi

Qai j h

" #ðMAÞ

maxsdz0

ðsd−cÞXi

Ehi½Qd

i �" #

ðMDÞ

maxsmz0

ðsm−cÞXi

Ehi½Qm

i jp�" #

ðMMÞ

In the truthful forecast sharing case (MA), the ma-nufacturer shares the retailers' forecasts and so canprecisely update her belief on all the retailers' demanddistributions and infer retailers' order quantities. Asingle wholesale price is set. In (MD), the manufacturerdoes not have any information about retailers' orders,yet also sets a single wholesale price. She takes theexpectations over her prior beliefs about all the retailers'private signal distributions. In the market-coordinatedforecast sharing case (MM) the manufacturer sets acontingent wholesale price based on her rationalexpectation of the aggregate order quantity conditionalon the current index price p. Since the manufacturerdoes not know each retailer's private forecast, she infersit from the public observed index price p. The followingproposition compares the manufacturer's pricing de-cisions under different supply chain informationstructures.


Proposition 3. The manufacturer's wholesale pricesunder supply chain structures A, D, and M have thefollowing relations:

( a ) s a is strictly increasing with θ . If h za ðNsd þ sÞðTd −Ta Þ þ bl ½ ðNsd þ sÞTd − sTa �

bNsdTa; then

sa≥ sd. Otherwise, sa<sd.(b) sm is strictly increasing with p. If pz a

bTd−Tm

Tmþ l

Td

Tm,

then sm≥sd. Otherwise, sm<sd.

(c) If h zTmðaþ bpÞðNsd þ sÞ−Ta½aNsd þ sðaþ blÞ�

bNsdTa; then

sa≥ sm. Otherwise, sa<sm.

where a¼P Ni¼1

ai; b¼P N

i¼1bi; and T j ¼ P N

i¼11ffiffiffis ji

p� �−1

for j ¼ a; d;m:

Proposition 3 details the conditions related to themanufacturer's pricing decision. Both 3(a) and 3(b) saythat under truthful forecast sharing or macro predictionmarket-coordinated forecast sharing, there is a criticalfractile above which the manufacturer will tend to set ahigher wholesale price in supply chain Structure A andMthan in Structure D. Proposition 3(c) further characterizesthe relationship between aggregate signal θ and indexmarket price p: a low indexmarket price is likely to induce alow sm, and vice versa.

The wholesale price increases in both truthful forecastsignal θ and the index price p since higher values reflect anaggregate perception of a prosperousmacro economy in thefuture. Themanufacturer thus expects to reapmore benefitsby charging a high wholesale price. In the same situation,retailers tend to place larger orders than what they wouldbased on just their own information. This seems to con-tradict the practice of quantity discounts, i.e., the higher theorder quantity, the lower the wholesale price. The un-derlying driving force of this result is due to the manu-facturer's confidence that the overall market condition isprosperous and her bargaining power in setting the marketprice. Although in such case the unit order cost increases,retailers can be compensated by the likely increaseddemand that is accurately predicted by themacro predictionmarket. In contrast, without the market prediction, theretailers will order according to their decentralized solu-tions. They face the opportunity cost of lost sales if demandsurges. Therefore, the retailer will still be able to earn a hightotal profit even with a lower unit profit margin.

On the contrary, if the aggregate forecast signal θ or theindexmarket price p is low, retailers will generally believethat the macro economy will worsen and so order less.The manufacturer may set a low price to encourage moreorders in such an economic downturn. This is also accu-rately predicted by the macro prediction market. In this

case, retailers' misfortunewill be essentially compensatedby the lower unit ordering price.

The index market price creditably conveys retailers'private forecasts about macro economy uncertainty. De-mand forecast sharing among the manufacturer andretailers is achieved indirectly via the macro predictionmarket. The manufacturer can control retailers' ordervariance by adjusting the price in a direction that issocially desirable from the perspective of the supplychain. This adjustment is especially important inreducing the bullwhip effect.

4. The value of forecast sharing

We investigate two aspects of forecast sharing in thissection: the impact on retailers' order variance and theexpected supply chain efficiency.

4.1. The order variance

Retailers experience demand uncertainty from custo-mers, but themanufacturer experiences it from the retailers.The manufacturer's decision making improves as retaileraggregate order variance drops. Under truthful forecastsharing, there is no order variance because themanufacturerprecisely observes retailers' demand forecast thus perfectlyinfers their order quantities. When forecast sharing is un-available, the decentralized order variances vary accordingto the different retailer signals. The macro prediction mar-ket significantly helps the manufacturer improve her in-ferred order accuracy.

Proposition 4. Var(Qim|p) < Var(Qi

d); Var(Qim|p)

decreases inM; limMYl VarðQmi jpÞ ¼ VarðQa

i j h Þ ¼ 0:

Macro prediction market coordination helps reduceorder variance because retailers can more accurately fore-cast themacro economy and their owndemand uncertainty.The manufacturer can also make more accurate inferencesabout the macro economy. The macro prediction marketinduces less supply chain order variance whenmore usefulinformation about the macro factor is incorporated. If themacro prediction market is precise enough, it can replicatetruthful forecast sharing as order variance disappears. Thishas important implications for the bullwhip effect. Thiswell-known informational problem is often represented bythe observed increasing order variances from downstreampartners in the supply chain. The literature has identifiedpotential sources of the bullwhip effect but has not offeredan effective solution to reduce the effect by properly ma-naging conflicting incentives among supply chain partners.Our macro prediction market-coordinated supply chainstructure can alleviate this effect. Note that by imposing a


correlation across the consumer markets, potentially thereis another dimension of the bullwhip effect— the rationinggame (see Ref. [22]). We don't deal with this problem inthis paper since we do not assume capacity constraints ofthe manufacturer.

4.2. The expected supply chain profit

A decentralized supply chain solution is generally sub-optimal to an integrated, first-best solution. A first-bestsolution, which is usually impossible, requires the manu-facturer to set the wholesale price equal to the marginalproduction cost. A number of articles on supply chaincoordination discuss the use of more complex non-linearpricing contracts or real options contracts to achieve thefirst-best solution [7]. However, we are most interested indetermining the best supply chain structure under thesimple price-only contract, the most common contract for-mat in the supply chain practice. We are interested in eval-uating the impact of information sharing on overall supplychain efficiency.

The total expected supply chain profit is determinedby the sum of all supply chain partners' expected profits.Under the supply chain structures A, D, and M, theexpected supply chain profit can be expressed as

EPj ¼XNi¼1

EΠ jR þ EΠ j

M

¼ ðr−cÞEXNi¼1

Q ji

" #−rE

XNi¼1

Ci;jðQ ji Þ;

where Ci;jðQ ji Þ ¼

1ffiffiffiffiffisdi

p Z �tj

−lUðtÞdt; j ¼ a; d;m; and tj ¼ U−1 s j

r

� �:

Proposition 5. If min(sd, sm, sa)≥ r/2>c, then theexpected supply chain profit satisfies EΠa>EΠd,EΠm>EΠd, and limMYl EPm ¼ limNYl EPa.

Proposition 5 shows the value of information sharingin the supply chain. Under the condition min(sd, sm,sa)≥ r/2>c the expected supply chain profits underStructure A and M are greater than profits under StructureD. This condition is not hard to be satisfied. Since themanufacturer is the Stackelberg leader in the game, it is nota surprise that she will charge a wholesale price at least halfof the retail price leaving retailers a smaller profit margin.Most industry products have retail prices less than twotimes the wholesale price. Compared to the decentralizedsupply chain, introducing the macro prediction market willimprove supply chain efficiency by increasing the total pieto be divided, and the manufacturer's expected profit willincrease since she has all the bargaining power. Retailers,however, may not benefit since the market condition

affects the manufacturer's pricing decision as well as thedivision of total supply chain surplus. Retailers' expectedpositive profits as a return of their private knowledge willattract them to trade in the macro prediction marketregardless of the market condition.

Total supply chain efficiency depends on marketliquidity and information transparency, i.e., how muchuseful information about the macro factor can beforecasted and revealed to the supply chain partners. Ingeneral, whether the macro prediction market-coordi-nated supply chain efficiency will outperform theaggregate supply chain efficiency depends on thetradeoff between the level of information asymmetryand prediction precision. On the one hand, the aggregatesupply chain has no information asymmetry and willtend to outperform the market prediction. On the otherhand, the market prediction can incorporate usefuloutside information and so be more precise. Whenboth the number of informed traders in the market andthe number of retailers approach infinity, the supplychain structuresM and Ayield the same expected profits.

The traditional supply chain literature considers theincentive and coordination issues within a closed system.Our work sheds new light on this area because of theadditional benefits generated outside the supply chainsystem. Since the market is an open system, one retailer'snon-participation decision will not compromise theinformation aggregation. But retailers who believe themarket efficiently predicts the macro factor will tend toincorporate the market price information into their orderdecisions. Our proposed framework aligns retailers' in-centives to share information and explores the value ofuseful information from other sources to increase overallsupply chain efficiency.

5. Extensions and discussions

We consider extensions of our model in this section.First, we investigate how retailers' changing risk pre-ferences influence their trading strategies. Second, wecharacterize the retailer's Pareto improving macro pre-diction market trading strategy. Third, we extend the indextrading to the index-based derivative trading to demon-strate that our proposed macro prediction market structurecan support supply chain risk management in corporatepractice. Finally, we discuss the impact of the macro pre-diction market construction on moral hazard problems.

5.1. The risk-averse retailer

Retailers' supply chain order strategy and macropredictionmarket trading strategy are perfectly separable


when they are risk-neutral. Their incentives to tradecome from their superior knowledge about future uncer-tainty of the economy. No arbitrage opportunities existunder the REE framework. In equilibrium, no contingentclaim matters to the retailers because they expect to paythe “average” value of the contingent claim based on thecommon market belief. Consequently, retailers cannotmake extra money by trading more complex financialcontracts. Since risk-neutral retailers only care about themean effect of their profit, their strategy is simply to tradethe index.

Retailers prefer to purchase the contingent claim as atype of insurance when they are risk-averse. A keycomponent in our model is the retailer's piecewise-linear payoff function, and a kink occurs when thedemand equals order quantity. This type of payofffunction can be hedged via writing covered call optionson the retail index [17]. Given the retailer's orderquantity Qi, trading the contingent claim is a Paretoimproving strategy because the retailer's expectedoverall profit is the same in both the macro predictionmarket and the commodity market. However, optionscan cancel off some uncertainty thus reducing the profitvariance. The contingent claim can be expressed as:

fi ¼ −rmin½Qi; ai þ bih� ¼ rmax½−Qi;−ai−bih�¼ −rai−rbihþ rmax½−Qi þ ai þ bih; 0�¼ −rai−rbihþ rðai þ bih−QiÞþ

¼ −rai−rbihþ rbi h−Qi−aibi

� �þ

The contingent claim can be generated by borrowingrai shares of riskless bonds and short selling rbi shares ofthe index and long the same shares of call option withstrike price Ki ¼ Qi−ai

bi.

Proposition 6. A risk-averse retailer's Pareto improvingmacro prediction market strategy when ordering Qi in thesupply chain is to borrow rai shares of riskless bonds andshort rbi shares of the index θ and long rbi shares of calloption with strike price Ki ¼ Qi−ai

bi.

This insurance can deal with the supply chainoperation and macro prediction market uncertainty bysmoothing out the total payoff from both. The futureindex price is positively correlated with the retailer'sconsumer market demand, so the retailer may face a lossin her consumer market if it goes down. However, theretailer can earn a positive profit in the macro predictionmarket by short selling. If the future index price goes up,the retailer will not have enough inventory to coverdemand and will lose in both the macro prediction

market and the consumer market. However, this loss canbe covered by the call options at hand. In any case, theretailer's risk exposure can be effectively hedged.

In the newsvendor model it is clear that risk-averseretailers will order less than the expected value-maximizing quantity [11]. It was shown that, undervery general conditions, the risk-averse retailer'soptimal ordering quantity increases with hedging [13].Therefore, opportunities for options trading helpoptimize retailers' inventory decisions.

5.2. The impact of the macro prediction market

Our macro prediction market-coordinated supplychain framework can bring risk management into cor-porate business practice. In the supply chain literature,risk sharing and transfer are obtained by bilateral con-tract commitments. Examples of widely used contractforms include reorder/buy back contracts [28], non-linear pricing/quantity discount policy [32], and lineartransfer payments [6]. It was shown in [3] that all thesecontracts can be classified as real options contracts.However, the question of whether the options contractscan be properly priced remains unanswered. Following-on work [5] proposed pricing real options in a bilateralcontract using Arrow–Debreu securities. We extend thepricing of options contract in a market setting withmultiple market players. Our proposed options contractsare based on a risky security (the retail index) withcontinuous payoffs. This is more realistic than usingArrow–Debreu securities.

Options contracts can provide retailers insurance todeal with operational risk. However, insurance may causea moral hazard problem since the retailers may not takesocially conscious actions when they feel economicallysecure.Moral hazard problems have beenwell-understoodin economics [15] but are generally overlooked in thesupply chain literature. For example, when the market isuncertain, a manufacturer may provide retailers with a putoption allowing them to sell back unsold products at a pre-specified salvage value (the strike price). The retailer maynot put much effort into selling products if the promotioncost is higher than its opportunity loss. All bilateral realoptions contracts suffer this problem. One possible solu-tion is to write contracts based on macro factors that cor-relate with the retailer's hedging needs but are not underthe retailer's control. Trading indices or index-based deri-vatives can solve these problems since they are simplycontingent claims written on the macro factor (the index).The retailers still incur residual risk in the marketplace. Inaddition, options trading can solve the market participa-tion problem since there might be experts who are


unwilling to trade in the macro prediction market for fearof financial losses. Buying or selling options withpreferred strike prices can afford these experts a measureof protection.

6. Conclusion

The Internet has facilitated real-time information accessacross organizations, making it possible to integrate thatinformation into decision models. While research on sup-ply chain information systems design has focused on tech-nological efficiency, such as XML-based workflow anddatabase integration, our innovation is to build a macroprediction market into organizations' evolutionary infor-mation systems design to encourage information sharingand aid supply chain decision making. We show that themacro prediction market can be used to reduce thebullwhip effect in the supply chain. In addition, the marketallows anyone with information to trade. More completeinformation makes the supply chain more efficient. Wethus provide important insights in designing market-basedinformation systems in guiding the structure of supplychain interactions.

We examine the impact of introducing a new type ofmarket – a macro prediction market – on supply chaininformation sharing and decision making. We also makeunique contributions to the emerging fields of predictionmarket and macro hedging market research. Predictionmarkets are indirectly influenced by financial markets. Thesignificance of these markets is still limited to predictingelections, sport trades, and other utility stocks and no clearresource allocation issue has yet been studied. In contrast toexisting research, we look at a concrete application in theclass of supply chain problems to validate the significanceof prediction markets for decision support in businesspractice.

In the macro hedging market literature, the key to hed-ging risk is sharing risk. Supply chain partners tend to actstrategically in providing information due to payoff asym-metry thus preventing effective risk sharing. The strategyof creating macro indices to trade instead of trading phy-sical products has a number of advantages. First, the tra-ding asset is broad enough to attract sufficient liquidity inthe market. The liquidity problem has been identified as animportant reason for the failure of many B2B markets.Many industrial products are not suitable for market tra-ding because of a lack of homogeneity. In addition, con-tracts specifying different quality, delivery times and otherfeatures are usually negotiated between buyer and seller,and so generate high transaction costs. Index-related fi-nancial contracts, in contrast, are essentially homogeneousproducts that can be traded with sufficient liquidity. Risk-

pooling can be realized without costly negotiation andcontract enforcement between parties. Therefore, the crea-tion of the macro prediction market makes possible thesharing of economic risks. The macro index-related finan-cial contracts are also general enough to reduce the moralhazard problems arising from bilateral insurance contracts.

Certain limitations apply to this paper. We assume theretail prices are exogenously given and are the same forall retailers. Endogenizing the pricing decision is aninteresting research question that can be studied in thefuture. Allowing different retailers to charge differentretail prices sounds a more realistic relaxation. In thecase of heterogeneous retail prices the manufacturer canbe expected to also set heterogeneous wholesale prices.

Future work could extend this research to cases withmultiple manufacturers and retailers. The construction ofthe index should also be studied. Different indices could bedesigned to represent a variety of products or tangible/intangible assets in the supply chain network. The indicescould be further distinguished to reflect regional envi-ronmental economic risks. More innovative and complexfinancial instruments, such as index-based derivatives, canalso be introduced for risk hedging purposes. In addition,future researchers can extend our findings to other businessapplications.

Acknowledgment

This paper was presented at several seminarsincluding those at the University of Texas at Austin,University of Alberta, National University of Singapore,City University of New York — Baruch College, andUniversity of Maryland, Baltimore County. We appre-ciate valuable feedback from seminar participants. Weespecially thank Anant Balakrishnan and Steve Gilbertfor their helpful comments and suggestions. The authorstake responsibility for all errors.

Appendix A

Sketch of Proof of Proposition 1. We look for a linearequilibrium of the form

lmi ¼ a0 þ a1 hi þa2ppi ¼ b0 þ b1l

mi þ b2p

pðyÞ ¼ k0 þ k1y

8<: ð1Þ

FOC w.r.t. πi from Eq. (I) together with the equalityin Eq. (II) we have the following

b0 ¼ 0; b1 ¼1k1

; b2 ¼ −1k1

ð2Þ


p¼ k0 þMa0M þ 1−Ma2

þ a1M þ 1−Ma2

XMi¼1

hi

þ k1M þ 1−Ma2

XuA0 þ Ai

XMi¼1

hi þ XL

!ð3Þ

where L ¼ a1k1. So A0 ¼ k0 þMa0

M þ 1−Ma2and A1 ¼ a1

M þ 1−Ma2,

which are constants for given M.To ensure that Eq. (I) is a well-behaved concave func-

tion of πi, SOC w.r.t. πi from Eq. (I) yields λ1>0.To solve theREE,weonlyneed to solve for constantsα0,α1,

α2, λ0, and λ1. From Eq. (3) and Normal Learning Theorem,p ¼ E hjPM

i¼1hi þ X

L

h i¼ sl

sþM2spþ MspsþM2sp

ðM þ 1−Ma2Þp−ðk0 þMa0Þa1

,

where sp ¼ Msdþ 1

L2sX

� �−1.

Rearranging terms and comparing with p(y)=λ0+λ1y yields

a1ðsþM 2spÞ ¼ MspðM þ 1−Ma2Þ ð4Þ

a1sl ¼ Mspðk0 þMa0Þ ð5ÞBelief update by the Normal Learning Theorem

yields

lmi uE hj hi; h−i þ X

L

" #¼ sl



h−i þ X

L

!;

where sv ¼ M−1sd

þ 1L2sX

� �−1.

Substituting Eq. (3) into μim yields

a0 ¼ a1sl−ðM−1Þðk0 þMa0Þsva1½sþ sd þ ðM−1Þ2sv�

ð6Þ

a1 ¼ sd−ðM−1Þsvsþ sd þ ðM−1Þ2sv

ð7Þ

a2 ¼ ðM−1ÞðM þ 1−Ma2Þsva1½sþ sd þ ðM−1Þ2sv�

ð8Þ

Since we have 5 unknowns α0, α1, α2, λ0, and L in thesystem of Eqs. (4)–(8). So it's solvable.

We suppress the expressions for all other parametersbut L:

L ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið5M 2−4Þs2 þ ð4M−2ÞM2ssd þM2s2d

q−Mðsþ sdÞ

2ðsþMsdÞMðM−1ÞsX

vuutsd

ð9Þ

So L is a uniquely determined constant for given M.Define k0=β0+β2p, and k1=β1, then πi|p=k0+k1θi.

So at the equilibrium price an agent's order strategy isinformation revealing. □

Proof of Proposition 2.

PIu1

Var½hjp� ¼1

Var hjPMi¼1

hi þ XL

¼ sþM 2sp

¼ sþM 2 L2sX sdML2sX þ sd

Substituting L2 from Eq. (9) and consider N→∞yields

limMYl

PI ¼ limMYl

s

þ Msd

1þ 2ðsþMsdÞðM−1Þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið5M2−4Þs2þð4M−2ÞM2ssdþM2s2d

p−MðsþsdÞ

¼ l

limMYl

p ¼ E hjXMi¼1

hi þ XL

" #

¼ slsþM 2sp

þ MspsþM 2sp

XMi¼1

hi þ XL

!¼ h

This completes the proof. □

Proof of Lemma 1. Since we formulate the retailer'sproblem as the traditional newsvendor problem, thenewsvendor solutions give us Q j

i ¼ F−1i; j 1− s j

r

� �, j=a,d,

m, where Fi,j(·) denote the forecasted demand distribu-tion by retailer i under scenario j. Normalizing theexpression we write it as Q j

i ¼ ai þ bilji þ 1ffiffiffiffi

s ji

q U−1 1−s j

r

� �where μi

j andffiffiffiffiffis ji

qare derived as follows:

Recall that h ¼ 1N

X N

i¼1hi. It's easy to verify that θ is

normally distributed, h fN l; 1s þ 1Nsd

� �.

Based on the Normal Learning Theorem, the beliefupdate yields

lai uE½hj h � ¼ sNsd þ s

lþ NsdNsd þ s

h

ldi uE½hj hi� ¼ ssþ sd

lþ sdsþ sd

hi

lmi uE hj hi; h−i þ XL

" #¼ sl



h−i þ XL

!;


where sv ¼ M−1sd

þ 1L2sX

� �−1.

Var½Dij h � ¼ b2iVar½hj h � þ1se

¼ b2isþ Nsd

þ 1seu

1sai

Var½Dij hi� ¼ b2iVar½hj hi� þ1se

¼ b2isþ sd

þ 1seu

1

sdi

Var½Dij hi; p� ¼ b2iVar½hj hi; p� þ1se

¼ b2isþ sd þ ðM−1Þ2sv

þ 1seu

1smi

This concludes the proof. □

Proof of Lemma 2 and 3. Results are directly obtainedby Lemma 1 and Eq. (9). □


Qai j h ¼ ai þ bi

sNsd þ s

lþ NsdNsd þ s

h

þ 1ffiffiffiffiffisai

p U−1 1−sa

r

� �ð10Þ

Ehi½Qd

i � ¼ ai þ biEhi½ldi � þ

1ffiffiffiffiffisdi

p U−1 1−sd

r

� �

¼ ai þ bilþ 1ffiffiffiffiffisdi

p U−1 1−sd

r

� �ð11Þ

Ehi½Qm

i jp� ¼ ai þ biEhi½lmi jp�

þ 1ffiffiffiffiffismi

p U−1 1−sm

r

� �¼ ai þ bip

þ 1ffiffiffiffiffismi

p U−1 1−sm

r

� �ð12Þ

Note that μim=E[θ|θi,p], and Eθi[μi

m|p]=Eθi[E[θ|θi,p]]=E[θ|p]=p. Substituting Eqs. (10)–(12) into (MA), (MD),(MM) and taking FOC w.r.t. s j, for j=a, d, m, we have

U−1 1−sa

r

� �þ Ta aþ b

sNsd þ s

lþ NsdNsd þ s

h

� �

¼ sa−cr

� �1

/ U−1 1− sar

� �� ð13Þ

U−1 1−sd

r

� �þ Tdðaþ blÞ ¼ sd−c

r

� �1

/ U−1 1− sdr

� �� ð14Þ

U−1 1−sm

r

� �þ Tmðaþ bpÞ ¼ sm−c

r

� �1

/ U−1 1− smr

� �� ð15Þ

where a ¼PNi¼1 ai; b ¼PN

i¼1 bi; and Tj ¼ PNi¼1

1ffiffiffisji

p� �−1

for j=a,m,d.Let x0=c / r, xj= s

j / r, tj=Φ−1(xj), for j=a,d,m. Using

the equality Φ−1(1−xj)=−Φ−1(xj) and, simplifying theexpression, we derive

Ta aþ bs

Nsd þ slþ Nsd

Nsd þ sh

� �

¼ UðtaÞ−x0/ðtaÞ þ ta ð16Þ

Tdðaþ blÞ ¼ UðtdÞ−x0/ðtdÞ þ td ð17Þ

Tmðaþ bpÞ ¼ UðtmÞ−x0/ðtmÞ þ tm ð18Þ

Let gðtÞ ¼ UðtÞ−x0/ðtÞ þ t. Then g VðtÞ ¼ /ðtÞ/ðtÞ−ðUðtÞ−x0Þ/ VðtÞ

/2ðtÞ þ

1 ¼ 2þ tðUðtÞ−x0Þ/ðtÞ , where the second equality follows by

the fact that /′(t) =− t/(t). Since Φ(t) is strictlyincreasing and /(t) is a strictly decreasing function oft when t≥0, g′′(t)>0 for t≥0. We also know that tj isstrictly increasing with sj.

Comparing Eqs. (16), (17) and (18), we derive all theresults for (a) – (c). □


VarðQdi Þ ¼ b2iVarðldi Þ ¼

b2i s2d

ðsþ sdÞ2VarðhiÞ

¼ b2i s2d

ðsþ sdÞ2d

1sþ 1sd

� �¼ b2i sd

sðsþ sdÞ

VarðQmi jpÞ ¼ b2iVarðlmi jpÞ

¼ b2isd−ðM−1Þsp

sþsd þ ðM−1Þ2sp

" #21sþ 1sd

� �

Comparing equations yields Var(Qid)≥Var(Qi

m|p)with equality holds when M=1. So Var(Qi

d)>Var(Qim|

p) when M≥2.Note that VarðQm

i jpÞ ¼b2i s

3dðsþ sdÞ

s½ððM−1ÞL2sX þ sdÞðsþ sdÞ þ ðM−1Þ2L2sX sd�2,

substituting Eq. (9) we can see it is a decreasing functionof M. limMYl VarðQm

i Þ ¼ 0. Clearly Var(Qia|θ ) =0

since full information sharing is imposed. □

Proof of Proposition 5. The expected supply chainprofits under Structure D, A, and M are

EPd ¼ ðr−cÞEXNi¼1

Qdi

" #−rXNi¼1

1ffiffiffiffiffisdi

p Z −td

−lUðtÞdt

¼ ðr−cÞ aþ bl−1Td

td

� �−

rTd

Z −td

−lUðtÞdt


EPm ¼ Ep ðr−cÞEXNi¼1

Qmi jp

" #−rXNi¼1

1ffiffiffiffiffismi

p Z �tm

−lUðtÞdt

( )

¼ ðr−cÞ aþ bl−1Tm

Etm

� �−Ep

rTm

Z �tm

−lUðtÞdt

EPa ¼ Eh ðr−cÞEXNi¼1

Qai j h

" #−rXNi¼1

1ffiffiffiffiffisai

p Z �ta

−lUðtÞdt

( )

¼ ðr−cÞ aþ bl−1Ta

Eta

� �−Eh

rTa

Z �ta

−lUðtÞdt

Therefore,

E½Pm−Pd� ¼ ðr−cÞ tdTd

−EtmTm

� �

þ rTd

Z �td

−lUðtÞdt−Ep

rTm

Z �tm

−lUðtÞdt

> ðr−cÞ tdTd

−EtmTm

� �−Ep

r

Tm

Z �tm

�td

UðtÞdt

> ðr−cÞ tdTd

−EtmTm

� �−

r2Tm

ð−Etm þ tdÞ

>r2−c

� � tdTd

−EtmTm

� �

where the next to the last inequality follows from thecondition minðsm; sdÞ > r

2so that −tm ¼ U−1 1− sm

r

� �< 0 and

−td ¼ U−1 1− sd

r

� �< 0. The last inequality requires that r

2> c.

By Eqs. (17) and (18), 1Td

gðtdÞ ¼ aþ bl ¼ aþ bEp ¼1Tm

EgðtmÞ > 1Tm

gðEtmÞ. The inequality follows by the strictconvexity of g(t) when t≥0. Note that g(0)≤0. For

k ¼ Td

Tm< 1, we have gðtdÞ > Td

TmgðEtmÞ > g

Td

TmEtm

� �. So

tdzTd

TmEtm. Therefore,E[Πm−Πd]>0. That is,EΠm>Πd.

E½Pa−Pd� ¼ ðr−cÞ tdTd

−EtaTa

� �

þ rTd

Z �td

−lUðtÞdt−E

h

rTa

Z �ta

−lUðtÞdt

> ðr−cÞ tdTd

−EtaTa

� �−E

h

rTa

Z �ta

�td

UðtÞdt

> ðr−cÞ tdTd

−EtaTa

� �−

r2Ta

ð−Eta þ tdÞ

>r2−c

� � tdTd

−EtaTa

� �

By Eqs. (16) and (17), 1Td

gðtdÞ ¼ aþ bl ¼ 1Ta

EgðtaÞ >1Ta

gðEtaÞ. Since τia>τid, T a>T d. For k ¼ Td

Ta< 1, we have� �

gðtdÞ > Td

TagðEtaÞ > g

Td

TaEta . Therefore, EΠ

a>EΠ d.

By Lemma 2, limMYl EXlmi ¼ limNYl lai ; andlimMYl smi ¼ limNYl sai . The same forecasts yieldthe same expected supply chain profits. □

Proof of Proposition 6. Under REE, trading optionsneither increases retailers' macro prediction market pro-fit nor affects their order quantity; the expected mean ofretailers' profit is the same. However, by smoothing offthe uncertain payoff function, the variance of wealth isdecreased. It is a Pareto improving strategy for riskaverse retailers. □

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Zhiling Guo is an Assistant Professor of Information Systems atUMBC (University of Maryland, Baltimore County). Her researchinterests include electronic commerce, financial markets, informationeconomics, and supply chain management. She has a Ph.D. inManagement Information Systems from the University of Texas atAustin.

Fang Fang is an Assistant Professor in the College of BusinessAdministration at California State University at San Marcos. Herresearch interests include knowledge markets, financial markets, andnetwork finance. She has a Ph.D. in Management Information Systemsfrom the University of Texas at Austin.

Andrew B. Whinston is a Professor of Information Systems,Economics, Computer Science, and Library and Information Sciences,Hugh Roy Cullen Centennial Chair in Business Administration, anddirector of the Center for Research in Electronic Commerce at theUniversity of Texas, Austin. He has published more than 300 papers intop-rated scientific journals and has recently co-authored the followingbooks: The Frontiers of Electronic Commerce, Electronic Commerce:A Manager’s Guide, The Economics of Electronic Commerce, TheInternet Economy: Technology and Practice, and Electronic Com-merce and the Revolution in Financial Markets.

supply chain information sharing in a macro prediction market

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