The Impact of Social Network Structures on Prediction Market Accuracy in the Presence of Insider Information

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1 The Impact of Social Network Structures on Prediction Market Accuracy in the Presence of Insider Information Liangfei Qiu, Huaxia Rui, and Andrew B. Whinston Li a n g f e i Qiu is an assistant professor of information systems at the Warrington College of Business Administration, University of Florida. He received his Ph.D. in economics from the University of Texas at Austin. His current research focuses on theoretical and empirical studies of social networks, prediction markets, procurement auctions, and applied game theory. Hua x i a Ru i is an assistant professor of computers and information systems at the Simon School of Business, University of Rochester. He received his Ph.D. in information systems, risk, and operation management from McCombs School of Business at the University of Texas at Austin. Dr. Rui s research interests include the study of social media, online advertising, securitization, and operation management. Andrew B. Whinston is the Hugh Roy Cullen Centennial Chair in Business Administration, professor of information systems, computer science and economics, and director of the Center for Research in Electronic Commerce at the University of Texas at Austin. Dr. Whinston received his Ph.D. in economics from Carnegie Mellon University. He is the co-author or co-editor of 23 books and over 300 articles. Ab s t r ac t: This paper examines the effects of social network structures on prediction market accuracy in the presence of insider information through a randomized laboratory experiment. In the experiment, insider information is operationalized as signals on the state of nature with high precision. Motivated by the literature on insider information in the context of financial markets, we test and confirm two characterizations of insider information in the context of prediction markets: abnormal performance and less diffusion. Experimental results suggest that a more balanced social network structure is crucial to the success of prediction markets, whereas network structures akin to star networks are ill suited to prediction markets. As compared with other network structures, insider information has less positive effects on prediction market accuracy in star networks. We also find that the bias of the public information has a larger negative effect on prediction market accuracy in star networks. Ke y w o r d s a n d p h r a s e s: controlled experiment, insider information, prediction markets, social networks. Under the right circumstances, groups are remarkably intelligent, and are often smarter than the smartest people in them. [41, p. xiii] Journal of Management Information Systems / Summer 2014, Vol. 31, No. 1, pp M.E. Sharpe, Inc. All rights reserved. Permissions: ISSN (print) / ISSN X (online) DOI: /MIS

2 146 Qiu, Rui, and Whinston Th e w i s d o m o f c r o w d s is b a s e d o n t h e a s s u m p t i o n that valuable knowledge in social systems frequently exists only as dispersed opinions, and that aggregating dispersed information in the right way can produce accurate predictions. A prediction market provides a vivid illustration of the power of the wisdom of crowds [11, 23]. A prediction market is a betting market for future uncertain events, which can produce accurate predictions by collecting and aggregating dispersed information. The prediction market mechanisms provide a method of putting your money where your mouth is [19]. People place bets on events that they think are most likely to happen, thus revealing in a sense the nature of their private information and subsequent posterior beliefs. A prediction market is becoming a powerful tool in companies increasingly sophisticated toolboxes of predictive analytics. In numerous well-known prediction markets, participants are the general public without special knowledge on the prediction topics. For example, in the Hollywood Stock Exchange, a prediction market forecasts opening weekend box office success, and many people participate simply on the basis of the entertainment value [44]. In the Iowa Electronic Markets, participants are allowed to buy and sell shares of candidates in U.S. and even foreign elections. In such cases, highly accurate information on targeted events is generally not available to the public. In the past few years, many large firms such as Hewlett-Packard, Google, Microsoft, and Intel have experimented with internal prediction markets to improve business decisions and learn how employees exchange information [15]. In these internal prediction markets, participants are selected specifically from different parts of the business operation, and some of them may have highly accurate information about the targeted event. Such information, with high precision and possibly less diffusion among participants, mimics to a certain extent insider information in financial trading. Hence, we call such information insider information in prediction markets. Enterprises that wish to utilize prediction markets for decision support must consider various design factors [33]. The effects of social network structures and insider information on prediction market accuracy have been overlooked in the design of many internal prediction markets and have been minimally discussed in the literature [26]. The lack of relevant academic research and the rising popularity of internal prediction markets motivate us to explore the following research question: RQ: Does the structure of the underlying social network play a role in the performance of a prediction market in the presence of insider information? The role of insider information has been widely debated in the context of financial markets. In financial markets, corporate officers, directors, and large stockholders, who are commonly called insiders, have access to information superior to that of outsiders. Prior research has focused on the amount of special information insiders possess as well as in the profit they earn from such knowledge [17, 37, 42]. In general, insider information has two main characteristics: First, trading profits are greater for traders who possess insider information. Rogoff [37] found that the returns to the insiders are on average 9.5 percent greater than the return to the stock market as a whole. Second, there is a small number of people who can access inside informa-

3 Prediction Market Accuracy in the Presence of Insider Information 147 tion [31]. One clear message that arises from the debate is that insider information passed through social networks enables individuals to gather superior information and earn abnormal returns on their stock transactions. Using a laboratory experiment, we operationalized the concept of insider information in a prediction market context to study the effect of social network structure on prediction market performance in the presence of insider information. More specifically, we allowed participants to access information sources of differing quality: Participants could choose to acquire a high-precision signal at a high cost, a lowprecision signal at a low cost, or no signal. We designated the highly precise signals as insider information because of the experimental evidence that such signals have two characteristics analogous to those of insider information that were discussed above: 1 (1) participants who acquire high-precision signals have abnormal performance, and (2) as compared with participants who acquire low-precision signals, participants who acquire high-precision signals are much less likely to share the signals with others, hence significantly limiting the number of participants with access to such signals. Experimental results suggest that a more balanced social network structure is critical to the success of prediction markets, whereas network structures akin to star networks are ill suited to prediction markets. Although the availability of insider information improves prediction market accuracy, as compared with other network structures, insider information has less positive effects on market accuracy in a star network. We also find that the bias of the public information available to participants has a larger negative effect on prediction market accuracy for a star network than other types of networks. In the present study, we advance our understanding of critical features for internal prediction market design, such as network structures, insider information, and public information bias. A critical maintained assumption underlying laboratory experiments is that findings from the laboratory are likely to provide reliable inferences outside the laboratory. Contextual factors in experimental instructions are beyond the control of the experimenter and may have profound effects on the generalizability to real-world scenarios. One approach to effectively net out laboratory effects is to perform a difference-in-difference (DID) estimation strategy [32]. In the present work, we recognize the potential weaknesses of the laboratory experiments and identify the causal relationship between network structure and prediction market accuracy using a DID estimation. The rest of the paper is organized as follows. We review related literature in the second section. In the third section, we outline a simple analytical model that captures the strategic aspect of the experiment. We describe the experiment and present our analysis of the experimental results in the fourth section. In the fifth section, we conclude the paper. Literature Review In t h e p r e s e n t s t u d y, w e a d d to t h e r e s e a r c h o n i n f o r m at i o n s y s t e m s by offering a new perspective on social networks and prediction markets. In some recent theoretical

4 148 Qiu, Rui, and Whinston work, researchers examined the effect of information exchange and social networks on individual behavior and market performance. Qiu et al. [35, 36] found that the effect of social networks on prediction markets depends on the cost level of information acquisition. We depart from the literature by further exploring the effect of the underlying structure of a social network on prediction market accuracy and by considering the presence of insider information. More specifically, we first extend the theoretical model so that a participant can get better information by exerting more effort in a continuous fashion that leads to the concept of insider information. Consequently, in the present experiment, participants chose from acquiring a high-precision signal at a high cost, a low-precision signal at a low cost, or acquiring no signal. Such a setting allows us to study the effect of social network structures on prediction market accuracy in a richer environment. Han and Yang [25] highlighted the importance of information acquisition in examining the implications of information networks for financial markets: When information is exogenous, social communication improves market accuracy, but it hurts market accuracy when information is endogenous because of traders incentives to free-ride on informed friends. Our present study also contributes to existing literature on organizational structure. Social communications among employees has long been viewed as a crucial determinant of the optimal organizational structure. Cowgill et al. [15] showed that internal prediction markets provide insight into how organizations process information. They found correlated trading decisions among employees with social or work relationships. Csaszar and Eggers [16] investigated how the performance of information aggregation mechanisms depends on the organization structure. Other researchers have examined the effects of network structures using laboratory experiments. Charness et al. [10] performed an experimental test and investigated how network structures affect the outcomes and dynamics of bargaining. Carpenter et al. [8] and Rosenkranz and Weitzel [38] studied the impact of network structures on the effectiveness of mutual monitoring and punishment in a public goods game. Cassar and Rigdon [9] explored the effect that network structure has on trust and trustworthiness in bilateral exchange. In a field experiment capturing real-world characteristics of social networks, Bapna et al. [5] studied the effect of the strength of social ties on Facebook. To the best of our knowledge, our present study is the first to examine the effects of social network structures on prediction market accuracy through a laboratory experiment. Although internal prediction markets have been successfully leveraged in many companies, their adoption for decision support is quite modest. Understanding the effects of network structures and insider information can facilitate future design of internal prediction markets. A Simple Theoretical Model Ex t e n d i n g t h e t h e o r e t i c a l w o r k in Qiu e t a l. [36], we set up a simple model of an internal prediction market with a continuous form of information acquisition.

5 Prediction Market Accuracy in the Presence of Insider Information 149 A manager resorts to n participants (employees) to forecast the realization of a random variable V (V could be sales, profit, or a product s quality ratings). For ease of exposition, we refer to the manager as he and each participant as she. Participants in the internal prediction market are linked to each other according to an underlying social network. In an organization, the social network can be formed because employees work concurrently on the same project or share the same office [15]. The social network Γ = (N, L) is given by a finite set of participants in the internal prediction market N = {1, 2,..., n} and a set of friendship links L N N. The social connections between the participants are described by an n n dimensional matrix denoted by g {0, 1} n n such that 2 g ij = 1 0 if ( i, j) L otherwise. Let N i (g) = {j N: g ij = 1} represent the set of friends of participant i. The degree of participant i is the number of participant i s friends: k i (g) = #N i (g). In our model, the social network is considered as a random graph. Random graphs have been widely used in network analysis [1, 18, 20, 28]. They exhibit a variety of features found in empirical network studies. While random graphs miss social and economic incentives that underlie network formation, they are a primary tool in analyzing various observed networks [28]. The information structure of our prediction market model follows the standard assumptions in the finance literature [4, 45]: Before receiving any private information, the manager and the participants share a common prior on the distribution of V, given by V ~ N(V 0, 1/ρ V ), (1) where ρ V is the precision of the prior. Figure 1 shows the timeline. Each participant can observe an imperfect private signal and pass it to her friends: 3 S i = V + ε i, ε i ~ N(0, 1/ρ ε ), (2) where ρ ε is the precision of participant i s information source for i = 1, 2,..., n. The signals errors ε 1,..., ε n are independent across participants and are also independent of V. The acquisition of information is costly in a continuous form: the precision ρ ε is given by a continuous function ρ ε (m i ), where m i is the effort level of player i. We assume that ρ ε (m i ) > 0, and ρ ε (m i ) < 0. Hence, a participant gets better information by exerting more effort, but the marginal value of effort is decreasing. The cost of exerting effort is given by c(m i ), where c (m i ) > 0, c (m i ) > 0, c(0) = 0, c (0) = 0, and c(1) =. Participants exchange information over a social network. For simplicity, we assume that they can observe their direct friends information, but not that of their secondorder friends (friends friends). The manager designs a quadratic loss function 4 to elicit the private information of participants. A participant s payoff function is given by

6 150 Qiu, Rui, and Whinston Figure 1. Timeline a b(x i V ) 2 c(m i ), (3) where x i is the prediction reported by participant i, and b(x i V ) 2 is a quadratic penalty term for mistakes in the forecast. In the model, a participant follows a two-stage decision procedure. In the first stage, all of the participants decide the effort level of information acquisition simultaneously. In the second stage, a participant makes use of her signal, as well as of the signals of her friends, to report her best prediction. We first focus on the optimization problem in the second stage. In this stage, participant i s best prediction x i * depends on whether participant i and her friends acquire information; thus, x i * is a function of m i and m Ni (g), where m Ni (g) is the action profile of participant i s friends, and it represents participant i s friends effort levels of information acquisition. Following Galeotti et al. [20], we assume that each participant observes her own degree k i, which defines her type, but does not observe the degree or connections of any other participants in the network. Each participant s belief about the degree of her friends is given by Π( k i ) {1,..., k max } k i, where k max is the maximal possible degree, and {1,..., k max } k i is the set of the probability distribution on {1,..., k max } k i. For simplicity, we make an assumption that friends degrees are all stochastically independent, which means that participant i s degree is independent from the degree of one of her randomly selected friends. This assumption is true for many random networks, such as the ErdoÉs Rényi random graph [18]. A strategy of participant i is a measurable function m i : {1,..., k max } [0, 1]. This strategy simply says a participant observes her degree k i, and on the basis of this information she decides the effort level of information acquisition. We focus on symmetric Bayes Nash equilibria, where all participants follow the same strategy σ. We say that participant i s strategy σ i is nonincreasing if m i (k i ) m i (k i ) for each k i > k i. If the strategy is nonincreasing, the higher-degree participants exert a lower effort level to acquire information. Proposition 1 gives us the basic result of the Bayes Nash equilibrium.

7 Prediction Market Accuracy in the Presence of Insider Information 151 Proposition 1: There exists a symmetric Bayes Nash equilibrium such that the equilibrium effort level of information acquisition m i* (k i ) is nonincreasing in degree, k i. Furthermore, the expected payoffs are nondecreasing in degree. The proof is presented in Appendix A. Proposition 1 shows that the more friends a participant has, the less willing she is to acquire precise information. Here, well-connected participants exert lower effort but earn more than poorly connected participants. After the decision on information acquisition, each participant reports her best prediction. The purpose of prediction markets is to generate fairly accurate predictions of future events by aggregating the private information of a large population. Following the approach developed in Van Bruggen et al. [43], we assume that the manager adopts a simple averaging rule, and his prediction is 1/nΣ n x *. 5 i=1 i An Experimental Analysis on Network Structures, Insider Information, and Prediction Market Accuracy In t h i s s e c t i o n, w e e x a m i n e t h e e f f e c t o f s o c i a l n e t w o r k s t ru c t u r e s on prediction market accuracy under a controlled laboratory experiment. Our experimental results demonstrate that network structure has a significant impact on an individual s behavior regarding information acquisition and prediction market performance. The effect of insider information also crucially depends on network structures. We recruited 144 undergraduate students from a large university with no previous experience in prediction markets experiments. Each subject was given 15 minutes of instruction (the instructions can be found in Appendix B). Then, we conducted 4 experiment sessions consisting of 36 participants, each divided into 9 groups of 4 randomly assigned participants. The average earnings were $8.87 per person, including $5 for showing up. Experimental Design Similar to the setup of the theoretical model, the participants were essentially asked to predict a random variable V during the experiment. The common prior is given by Equation (1), and in the experiment we set V 0 = 10, and ρ V = 0.5. To make our experiment easy to understand, we modify the setup of information acquisition in the theoretical model. A participant has three possible choices for information acquisition after observing the number of connections she has: a high-precision signal (ρ ε = 2) costing $1, a low-precision signal (ρ ε = 1) costing $0.5, or no signal. As mentioned earlier, the higher-priced signal provides better information than the lower signal; therefore, we call this insider information. Since participants paying for the high-precision signal have the best knowledge of the market, we call them insiders. Once all the decisions of information acquisition are made, the participants are free to communicate over the given network. 6 The experiment was made up of four different treatments of network structures: (1) baseline treatment, nonnetworked

8 152 Qiu, Rui, and Whinston Figure 2. Network Structures environment; (2) star network; (3) circle network; and (4) complete network. They are illustrated in Figure 2. Following a large and growing number of experiments on network structures [8, 10, 38], the network size in our experiment is four. In network structures 1, 3, and 4, the permutation of network positions does not matter, and all the participants have equal degree. We call these network structures with equal degree. However, in the star network, the central participant is significantly more influential than anyone else. Despite their simplicity, these four drastically different network structures may enable us to clearly identify the effect of social network structures on prediction market performance. Our experiment ran on a computer system specifically designed for this study. Each subject was seated at a computer terminal. Throughout the experiment, the subjects were not allowed to communicate in person and could not see others screens. The only communication channel available to them was to chat via designated Gmail accounts. In the baseline treatment, N i (g) =, each participant was isolated. In the complete network, participant i was connected to three other participants (we call them participant i s friends ). Similarly, the communication networks are given by a star network and a circle network in Treatments 3 and 4, respectively. Note that a participant knows the exact number of her connections before she makes choices about information acquisition. Finally, the participants submitted their forecasts about V. After the experiment, the computer system calculated the total payoff of each participant according to the payoff function (3). We set a = 5 and b = 1. We were interested in testing the following hypotheses.

9 Prediction Market Accuracy in the Presence of Insider Information 153 Hypothesis 1: Each individual s information acquisition is nonincreasing in the participant s degree. Hypothesis 2: The participant s earnings are nondecreasing in the degree. H1 and H2 validate Proposition 1 in the analytical model and further examine the results in prior research [3] in the presence of insider information. Hypothesis 3: As compared with participants who acquire low-precision signals, participants who acquire high-precision signals are less likely to share information with others. Hypothesis 4a: The participants who acquire insider information have higher prediction accuracy. Hypothesis 4b: The participants who acquire insider information have higher earnings. H3, H4a, and H4b can be viewed as the characteristics of insider information [31, 37], and the support of them will justify our operationalization of the concept of insider information in prediction markets. In addition, H3 is related to the literature on information sharing [24], where it is found that scientists are less likely to share more valuable information about their research. In our context, participants are less willing to share the highly precise signals they purchased at a high cost. H4a and H4b are additionally motivated by the increasing literature on social networks and financial markets. In H4a and H4b, we examine the effect of insider information on the individual s prediction performance and earnings. Coval and Moskowitz [14] found that social networks help fund managers earn above-normal returns in nearby investments: The average fund manager generates an additional 2.67 percent return per year from local investments, relative to nonlocal holdings. Cohen et al. [12, 13] found that portfolio managers place larger concentrated bets on stocks they are connected to through their education network and do significantly better on these holdings relative to nonconnected holdings. Hypothesis 5: Star-networked prediction markets are significantly outperformed by other types of prediction markets. Hypothesis 6: As compared with other network structures, insider information has less positive effects on prediction market accuracy in a star network. Hypothesis 7: The bias of the public information available to participants has a larger negative effect on prediction market accuracy in a star network. H5, H6, and H7 examine the role that social network structures play in prediction markets. H5 and H6 are motivated by a large body of literature on network structures. In a laboratory experiment, Carpenter et al. [8] demonstrated that network structures have a significant impact on the behavior of subjects in public goods games. Golub and Jackson [21] theoretically showed that the existence of small prominent groups of opinion leaders is an obstacle to the wisdom of crowds. The wise crowd fails when

10 154 Qiu, Rui, and Whinston Table 1. Descriptive Statistics of the Participants Predictions Mean Standard deviation Minimum Maximum Observations Nonnetworked environment Star network Circle network Complete network one participant receives a substantial amount of attention from everyone and becomes significantly more influential than anyone else. The central participant in our star network is in a similar position among participants as the opinion leader in their model. Thus, the test of H5 and H6 in our experiments can also shed some light on empirical evidence of their theoretical predictions. Gruca and Berg [22] evaluated the effect of public information bias on prediction market accuracy. They found that when the public information has a bias, the forecasts generated by prediction markets will be more accurate than those generated by the public information. Motivated by monetary gains, prediction market participants have incentives to correct known biases in publicly available information. In this paper, we further examine the effect of public information bias under different network structures in H7. Because of the inefficient information aggregation of a star network [21], the negative effect of the public information bias is larger in star-networked prediction markets. The Effect of Degrees on Information Acquisition and Earnings Before we test H1 and H2, we first summarize in Table 1 the statistics of participants predictions under different network structures. 7 By calculating the standard deviations of predictions under different treatments, we find that the standard deviation under a complete network is significantly lower than the standard deviation under a nonnetworked environment (0.830 versus 1.530, p < 0.01), which suggests that communication leads to more consensus about the true value. In H1 we essentially examine whether participants information acquisition behavior is consistent with the equilibrium strategy; in H2 we examine whether more social connections lead to higher payoffs. To test these hypotheses, we first run a multinomial logit regression of participants information acquisition decisions on their degree. The three possible outcomes for information acquisition are acquiring a high-precision signal (acquisition = 2), acquiring a low-precision signal (acquisition = 1), and acquiring no signal (acquisition = 0). The explanatory variables are the number of connections (degree) and a dummy variable, sdummy, indicating whether the participant having three connections is in a star network. Participants having three connections can be

11 Prediction Market Accuracy in the Presence of Insider Information 155 Table 2. The Effect of Degree on Information Acquisition (Multinomial Logit Estimates) Dependent variable: acquisition Explanatory variables Low-precision signal (acquisition = 1) High-precision signal (acquisition = 2) degree 0.478** ( 2.326) 0.504** ( 2.533) sdummy 1.536** ( 2.270) 1.908* ( 1.661) Constant 0.998** (2.416) 1.213*** (3.024) Observations Pseudo R 2 : Notes: z-statistics are in parentheses. *** p < 0.01; ** p < 0.05; * p < 0.1. embedded either in a complete network or in a star network (the central participant), so we add sdummy in the regression. The results are given in Table 2. We find that participants information acquisition behavior is indeed consistent with the equilibrium strategy predicted by the analytical model: A larger number of connections leads to a lower probability of information acquisition. One more connection reduces the logodds between acquiring a low-precision signal and not acquiring a signal by 0.478, and reduces the log-odds between acquiring a high-precision signal and not acquiring a signal by Next, we run an ordinary least squares (OLS) regression of earnings on the degree, the cost of information acquisition, and the star network dummy variable: earnings i = b 0 + b 1 degree i + b 2 sdummy i + b 3 acquisition i + ε i. (4) Table 3 shows that the participants earnings increase with the degree. The coefficient on degree is significantly positive. Being excluded from the connections is thus a handicap for a participant. The control variables are a star network dummy variable, sdummy, and a variable, acquisition, indicating a participant s decision on information acquisition. A small sample size is a common problem for an experimental method. The validity of z statistics depends on the asymptotical distribution of large samples. When the sample size is insufficient for straightforward statistical inference, bootstrapping is useful for estimating the distribution of statistics without using asymptotic theory. In column 2 of Table 3, we use bootstrapping to compute the standard errors and find that the result is robust. 8 A striking pattern in the data is that earnings (without show-up fee) are remarkably skewed (skewness = 2.019). The percentage histogram for earnings is shown in Figure 3. Quantile regression analysis is particularly useful when the conditional distribution of earnings is not symmetric and does not have a standard shape [30]. The quantile

12 156 Qiu, Rui, and Whinston Table 3. The Effect of Degree on Participants Earnings Dependent variable: earnings (1) (2) Explanatory variables OLS Bootstrapping degree 0.130** (2.030) 0.130** (2.294) sdummy ( 0.465) ( 0.633) acquisition 0.256*** ( 2.859) 0.256** ( 2.475) Constant 3.968*** (23.67) 3.968*** (19.10) Observations R Notes: t-statistics are in parentheses. *** p < 0.01; ** p < 0.05; * p < 0.1. Figure 3. Percentage Histogram for Earnings regression models allow us to account for unobserved heterogeneity and heterogeneous covariates effects. In Figure 4, we plot the parameter estimates b 1 of the quantile regressions based on Equation (4). There are nine estimated quantile regressions with 0.1, 0.2,..., and 0.9 quantiles. The parameter estimates of the quantile regressions are connected by the solid line, with the shaded area being their 95 percent confidence intervals. The OLS effects estimate shown in Table 3 and its 95 percent confidence interval are plotted as horizontal lines in this figure. We find that the quantile regression parameter estimates decrease with quantiles in general. When the quantile is low, the quantile estimates are significantly positive. However, as the quantile increases,

13 Prediction Market Accuracy in the Presence of Insider Information 157 Figure 4. OLS and Quantile Regression Estimates for Model (4) the estimates decrease. This suggests that the impact of degree on earnings is more pronounced for lower quantiles. It is also interesting to observe that the confidence intervals of quantile regression estimates do not overlap with the OLS confidence interval for low quantiles. Therefore, the effect of degree on earnings is found to exist primarily at the lower quantiles of the earnings distribution, and the OLS estimate tends to underestimate this effect for lower quantiles. The experimental results in Tables 2 and 3 thus support H1 and H2. Because of the randomization of the network position assignments, our experimental results do not suffer from the identification problem related to the endogenous network structure and reveal causality rather than mere correlation. The Diffusion of Insider Information The effect of social networks on information diffusion and dissemination has been widely discussed in the literature [2, 27, 39, 40]. In our present experiment, the participants used the designated gmail accounts to communicate with each other. Using their chat information we can examine the diffusion of private signals with different precisions and test H3. We define the sharing percentage as the percentage of a participant s friends with whom the participant shares information. Figure 5 shows that participants who acquire high-precision signals are less likely to share information with their friends than participants who acquire low-precision signals. This implies that the diffusion of insider information is very limited and supports H3. This finding is consistent with a characteristic of insider information: The number of participants who can access insider information is much smaller than the number of

14 158 Qiu, Rui, and Whinston Figure 5. Average Sharing Percentages of Insider Information and of Low-Precision Signals outsiders [31]. This is one reason why we designate the highly precise information as insider information. To further examine the diffusion of insider information, we run an OLS regression as follows: share i = b 0 + b 1 degree i + b 2 sdummy i + b 3 insider i + ε i, (5) where share is the sharing percentage, and insider is a dummy variable indicating whether participant i receives insider information (a high-precision signal). The control variables are degree and sdummy. Note that in this regression, we exclude the participants who do not have friends or do not acquire information. Table 4 presents the regression results; we are interested in the coefficient b 3. In column 1, we find that receiving insider information significantly reduces participants willingness to share information: The average sharing percentage of insiders is 69.2 percent less than that of participants who acquire a low-precision signal after controlling for network structures. Column 2 shows that the result is robust when we use bootstrapping. The Effect of Insider Information on Individual Prediction Accuracy H4a predicts that participants who acquire insider information have higher prediction accuracy. Following Van Bruggen et al. [43], the prediction accuracy of participant i is given by accuracy i xi V = 1 Absolute Percentage Errori = 1, V

15 Prediction Market Accuracy in the Presence of Insider Information 159 Table 4. Estimate of the Diffusion of Insider Information Using Model (5) Dependent variable: share (1) (2) Explanatory variables OLS Bootstrapping degree 0.121** ( 2.082) 0.121* ( 1.901) sdummy (0.350) ( 0.633) insider 0.692*** ( 8.381) 0.692*** ( 9.023) Constant 1.202*** (9.722) 1.202*** (7.472) Observations R Notes: t- or z-statistics are in parentheses. *** p < 0.01; ** p < 0.05; * p < 0.1. Table 5. The Effect of Insider Information on Individual Prediction Accuracy Dependent variable: accuracy (1) (2) (3) Explanatory Variables OLS OLS Bootstrapping degree *** (3.768) *** (3.660) *** (3.976) sdummy ( 0.853) ( 0.833) ( 0.827) insider *** (4.607) *** (3.586) *** (3.274) lsignal (0.0907) (0.0808) Constant 0.909*** (135.7) 0.910*** (99.18) 0.910*** (86.70) Observations R Notes: t- or z-statistics are in parentheses. *** p < 0.01; ** p < 0.05; * p < 0.1. where x i is the prediction of participant i and V is the realization of the random variable in the corresponding prediction market. In Table 5, the dependent variable, accuracy, is the individual s prediction accuracy. The dummy variable, insider, indicates whether a participant acquires insider information. The variable lsignal denotes a dummy that is equal to one if a participant acquires a low-precision signal. The control variables are degree and sdummy. The regression model is given by the following equation: accuracy i = b 0 + b 1 degree i + b 2 sdummy i + b 3 insider i + b 4 lsignal i + ε i. (6)

16 160 Qiu, Rui, and Whinston The coefficient on insider is and significant. The coefficient implies that obtaining insider information in our experiment is associated with a roughly 3.28 percent increase in the focal participant s prediction accuracy. This experimental result is consistent with the empirical findings by Cohen et al. [13]: Analysts gain a comparative information advantage through their social networks. Coval and Moskowitz [14] showed that mutual fund managers earn abnormal returns in nearby investments. They think that mutual fund managers and local corporate executives run in the same circles, belong to the same country club, and so forth. This result is supported by the literature on insider information: Insider information allows insiders to obtain a higher than average rate of return in the market [37]. Our result is also robust to the use of bootstrapping in column 3 of Table 5. In column 2 of Table 5, the coefficient on lsignal is positive but not significant. This result shows that receiving a low-precision signal from others does not significantly improve the prediction performance. This is one reason why acquiring a low-precision signal is not considered as insider information. The low-precision signal is not precise enough to allow participants to perform significantly superior to others. If low-precision signals were also considered as insider information in the experiment, the empirical evidence would be inconsistent with the characterization of insider information. After all, the empirical basis for detecting insider information is the superior prediction performance and the abnormal return of insiders [34]. To consider the heterogeneous effects of insider information, we also run quantile regressions and plot the parameter estimates b 3 of the quantile regressions based on Equation (6) in Figure 6. Similarly, there are nine estimated quantile regressions with 0.1, 0.2,..., and 0.9 quantiles. The parameter estimates of the quantile regressions are connected by the solid line, with the shaded area being their 95 percent confidence intervals. The OLS effects estimate shown in Table 5 and its 95 percent confidence interval are plotted as horizontal lines on Figure 6. We find that when the quantile is low, the positive impact of insider information on prediction accuracy is more pronounced. H4b predicts that participants who acquire insider information have higher prediction accuracy. Similarly, we test H4b using the following model: earnings i = b 0 + b 1 degree i + b 2 sdummy i + b 3 insider i + b 4 lsignal i + ε i. (7) In Table 6, we find that the coefficient on insider is positive and significant, and the coefficient on lsignal is nonsignificant. This result supports H4b and also shows that acquiring a low-precision signal does not significantly improve the earnings. Our result is also robust to the use of bootstrapping in column 2. The Effect of Network Structures on Prediction Market Accuracy H5 predicts that prediction market accuracy depends crucially on network structures. In our experiment, each group is a prediction market, so we have a total of 36 prediction markets. The accuracy of prediction market g is measured by forecast accuracy:

17 Prediction Market Accuracy in the Presence of Insider Information 161 Figure 6. OLS and Quantile Regression Estimates for Model (6) Table 6. The Effect of Insider Information on Individual Earnings Dependent variable: earnings (1) (2) Explanatory variables OLS Bootstrapping degree 0.133** (2.054) 0.133** (2.320) sdummy ( 0.483) ( 0.652) insider 0.501*** (2.756) 0.501** (2.242) lsignal (1.030) (0.872) Constant 3.939*** (21.26) 3.939*** (16.15) Observations R Notes: t- or z-statistics are in parentheses. *** p < 0.01; ** p < 0.05; * p < 0.1. Mkt_Accuracy g Fg Vg = 1 Absolute Percentage Errorg = 1, V where F g is the forecast of prediction market g calculated as the average of all four participants predictions in that market (the manager s forecast accuracy) and V g is the realization of the random variable in market g. We perform a series of t tests, and g

18 162 Qiu, Rui, and Whinston the results suggest that a complete network prediction market and a circle-networked prediction market significantly outperforms a star-networked prediction market (t statistics: p = for complete versus star; p = for circle versus star). We also find that a complete-networked prediction market does not significantly outperform a circle network (t statistics: p = 0.29). We also adopt another commonly used measure, mean squared error (MSE), in evaluating prediction accuracy. The MSE for each type of network structure is given by the following equation: ( ) 1 9 MSE = F V 9 g= 1 s g g where s = 1, 2, 3, 4 (1: nonnetworked environment; 2: star network; 3: circle network; and 4: complete network; for each type of network structure, we have nine prediction markets). We compute the MSE for different network structures: MSE 1 = 0.268, MSE 2 = 0.421, MSE 3 = 0.274, and MSE 4 = (note that a higher MSE implies lower prediction accuracy). We find that star-networked prediction markets are outperformed by other types of prediction markets. Thus, our results are robust to different measures of prediction market accuracy. To further examine the effect of network structures on prediction market accuracy and test H5, we run the following regression: Mkt_Accuracy j = β 0 + β 1 cpl_mkt j + β 2 circle_mkt j + β 3 nonnet_mkt j + ε j, (8) where cpl_mkt is a dummy variable indicating whether a prediction market has a complete network, circle_mkt is a dummy variable indicating whether a prediction market has a circle network, and nonnet_mkt is a dummy variable indicating whether a prediction market is a nonnetworked prediction market. Columns 1 and 2 in Table 7 show that the coefficients on these three dummy variables are significantly positive. This result implies that star-networked prediction markets are significantly outperformed by other prediction markets in terms of prediction accuracy, and supports H5. H6 states that insider information contributes to prediction market accuracy, and the effect of insider information depends on network structures. In an experimental study, Qiu et al. [36] found that a complete-networked prediction market outperforms a nonnetworked prediction market in terms of forecast accuracy when the cost level of information acquisition is low. Here, we further explore the impact of network structures on the effect of insider information. To test H6, we use the difference-in-difference (DID) estimation strategy. The regression model is given by 2, Mkt_Accucy j = β 0 + β 1 Insider_mkt j + β 2 Star_mkt j + β 3 Insider_mkt j * Star_mkt j + ε j. (9) We present the estimation results from DID in Table 8. The independent variable Mkt_Accuracy is the prediction market accuracy. The explanatory variable Insider_mkt represents the number of insider information acquired in this market, and Star_mkt is a

19 Prediction Market Accuracy in the Presence of Insider Information 163 Table 7. The Effect of Network Structures on Prediction Market Accuracy Dependent variable: Mkt_Accuracy (1) (2) Explanatory variables OLS Bootstrapping cpl_mkt *** (3.590) *** (3.732) circle_mkt *** (4.652) *** (5.140) nonnet_mkt *** (4.771) *** (4.422) Constant 0.871*** (67.80) 0.871*** (65.91) Observations R Notes: t- or z-statistics are in parentheses. *** p < 0.01; ** p < 0.05; * p < 0.1. Table 8. The Effect of Insider Information on Prediction Market Accuracy Dependent variable: Mkt_Accuracy (1) (2) Explanatory variables OLS Bootstrapping Insider_mkt ** (2.293) ** (2.412) Star_mkt ** ( 2.504) ** ( 2.472) Insider_mkt * Star_mkt ** ( 2.269) ** ( 2.514) Constant 0.925*** (72.16) 0.925*** (71.88) Observations R Notes: t- or z-statistics are in parentheses. *** p < 0.01; ** p < 0.05; * p < 0.1. dummy variable indicating whether it is a star-networked prediction market. The coefficient on Insider_mkt is positive and significant. It means that the insider information has a positive effect on the prediction market accuracy under network structures with equal degrees. This is consistent with the result of Aktas et al. [3]: Insiders contribute to faster price discovery and market accuracy. The coefficient on the interaction term is the DID estimator. We use this identification strategy to estimate the effect of insider information under different network structures. The DID approach provides an unbiased estimate of the relative effect of insider information on market accuracy in a star network as compared with other network structures. Table 8 shows that the DID estimator is negative and significant. As

20 164 Qiu, Rui, and Whinston compared with other network structures, insider information has less positive effects on market accuracy under a star network. The basic result is also robust to the use of bootstrapping in column 2 of Table 8. There are two explanations for the poor performance of prediction markets with star networks. First, there is a high dependence of the performance of a star-networked prediction market on the functioning of the central hub. Whenever a participant receives information that has a substantial deviation from the truth, the dissemination of such biased information has a negative effect on the prediction market performance. In a star network, when the hub receives information with a substantial deviation from truth, such negative effects will exacerbate and hurt the prediction market performance significantly. Second, the simple averaging rule of information aggregation is inefficient for a star network. Even though the hub is in the perfect position to aggregate information from other peripheral participants and generates a more accurate prediction than other participants, by putting equal weight on all participants estimates the simple averaging rule fails to aggregate the estimates efficiently. We find that this inefficiency can reduce the positive impact of insider information on prediction market accuracy in star networks, which supports H6. Such inefficiency is less a concern in a more balanced social network structure. For example, if all participants have equal influence in their communication, such as a circle or a complete network, the simple averaging rule can aggregate information more efficiently. Acemoglu et al. [1] studied a model in which each individual receives a signal about the underlying state of the world and observes the past actions of a stochastically generated neighborhood of individuals (a random social graph). They showed that a finite group of excessively influential agents (like the central participant in our star network) is an obstacle to the wisdom of crowds. Therefore, our experimental result supports Acemoglu et al. s theoretical conclusions. Golub and Jackson [21] showed that large societies can be smart in the aggregate if people avoid concentrating too much on any small group of agents. A general condition is that the influential agent is vanishing as the number of agents grows. In our context, even if the network size is greater than four, the role of the central participant in a star network does not vanish. However, in a circle network or a complete network, each participant has equal influence, and as the number of participants grows, one particular participant s information does not affect the performance of a prediction market significantly. This experimental result has a direct managerial implication for the business practice of prediction markets: Managers should try to understand the social network structure among the employees to efficiently aggregate their information through internal prediction markets. For example, when the underlying social network structure is more balanced (i.e., employees are equally well connected to each other), then the simple averaging rule should work efficiently and the availability of insider information would be beneficial to the prediction accuracy. If some participants are significantly more well connected than most others, as in a star network, then the simple averaging rule may not work well and the availability of insider information would be less effective

21 Prediction Market Accuracy in the Presence of Insider Information 165 Table 9. The Effect of Public Information Bias on Prediction Market Accuracy Dependent variable: Mkt_Accuracy (1) (2) Explanatory variables OLS Bootstrapping Bias * ( 1.932) * ( 1.730) Star_mkt 0.142*** ( 5.580) 0.142** ( 2.451) Bias * Star_mkt 0.122*** ( 2.582) 0.122** ( 2.224) Constant 0.966*** (94.15) 0.966*** (96.99) Observations R Notes: t- or z-statistics are in parentheses. *** p < 0.01; ** p < 0.05; * p < 0.1. in improving prediction accuracy. Of course, identifying the true underlying social network structure within a large organization is itself a big challenge; nevertheless, it is beneficial to glean even a small amount of information about the network characteristics in order to guide the design of the prediction market. Cowgill et al. [15] found that several main factors can significantly influence information sharing among Google employees: physical office locations, joint-work relationships, and sharing a common non-english native language. Managers can use these proximity measures to infer social network structures within the organization and improve the design of internal prediction markets for decision support. The Effect of Public Information Bias on Prediction Market Accuracy H7 states that the negative effect of public information bias is more pronounced when the underlying network is a star topology. We test this hypothesis using the following regression model: Mkt_Accuracy j = β 0 + β 1 Bias j + β 2 Star_mkt j + β 3 Bias j * Star_mkt j + ε j. (10) We present the estimation results in Table 9. Similarly, the independent variable Mkt_Accuracy j is the prediction market accuracy. The explanatory variable Bias j is a variable measuring the public information bias of each prediction market. In our experiment, all participants share a common prior V ~ N(V 0, 1/ρ V ). However, the realization of V in each market, V j, could be different from the prior mean V 0. The public information bias is measured by the difference between the true value of V and the prior mean: Bias j = V j V 0. The coefficient on the interaction term β 3 is the DID estimator. The identification strategy here is similar to the one used in testing H6. Table 9 shows that β 3 is

22 166 Qiu, Rui, and Whinston significantly negative, and this result is robust when we do bootstrapping. As compared with other network structures, the negative effect of public information bias is much higher for a star network. Conclusion Alt h o u g h p r e d i c t i o n m a r k e t s h av e b e e n successfully a p p l i e d in many areas, they can fail and have been observed to produce misleading results [44]. It is thus critical to understand how to design an efficient information aggregation mechanism and consider various factors to minimize these failures. In this paper, we designed and carried out a laboratory experiment to examine the effect of social network structures on prediction market accuracy in the presence of insider information. We found that the effect of insider information depends crucially on network structures: As compared with other network structures, insider information has less positive effects on prediction market accuracy in a star network. The experimental results further suggest that the negative effect of public information bias is more pronounced when the underlying network is a star topology. The present study has several limitations. Experimental methods tend to impose a strictly controlled environment, and generalization of findings should be done with care. Although the network structures of size four are a useful metaphor for many market environments and have been adopted in a large body of prior literature (e.g., [8, 10, 38]), these basic network structures are overly simplistic. Thus, one important and interesting extension of our research will be to investigate additional networks of larger sizes. Our experiment does not account for the security trading mechanism, which is becoming another important prediction market mechanism and is a natural extension of this work. Another limitation of this study is the artificial network design. In our present experiments, the participants have no real social connections with their assigned friends. Actually, it is difficult to envision a laboratory study that fully mirrors the circumstances of the external environment of interest. Although laboratory studies may not promise quantitative external validity, they do promise qualitative external validity if the observed relationship is monotonic and does not change direction when changing the level of variables seen in the field relative to those in the laboratory [29]. By focusing on qualitative rather than quantitative insights, our present study uncovers general effects of insider information and network structures on prediction market accuracy. A further research direction is to conduct a hybrid laboratory-field experiment [6]. In our context, a randomized field experiment can address the concern of artificial networks, but it suffers from a lack of strict environmental and contextual controls. The control provided by the laboratory allows us to strip away many confounding factors in the field. A hybrid experiment leverages the advantages of both. By recruiting individuals and their real social network peers in the laboratory instead of employing artificial networks, one can further examine the effects of real social network structures on prediction market accuracy.

23 Prediction Market Accuracy in the Presence of Insider Information 167 Not e s 1. We explain this further in the section of experimental analysis. 2. For simplicity, we assume the network is undirected, but the results also hold for directed networks. 3. This is similar to the setup in [7]. We assume that people make choices about information acquisition first, and after that, they exchange information informally according to reciprocity and norms of fairness. The exchange theory explains the reciprocity based on the idea of socially embedded behavior. 4. We can also use other strictly proper scoring rules; see [19]. The qualitative results remain unchanged. 5. Csaszar and Eggers [16] show that averaging estimates can be the most effective method under some circumstances. 6. After the experiment, we checked the participants chat history and found that no one misreported the private signal to others. 7. Note that there is an outlier who predicted 2 in a nonnetworked environment. If we exclude this outlier, the standard deviation of predictions under a nonnetworked environment is 0.91 and is still significantly higher than those under other network structures. One may also notice that there is a trend that the mean of the participants predictions increases with the network connectivity. This is simply because the realization of V in each prediction market could be different. Accidentally, the average realization of V increases with the network connectivity. 8. We draw a sample of 144 observations with replacement, and repeat this process 10,000 times to compute the bootstrapped standard errors. Re f e r e n c e s 1. Acemoglu, D.; Dahleh, M.A.; Lobel, I.; and Ozdaglar, A. Bayesian learning in social networks. Review of Economic Studies, 78, 4 (2011), Adomavicius, G.; Gupta, A.; and Sanyal, P. Effect of information feedback on the outcomes and dynamics of multisourcing multiattribute procurement auctions. Journal of Management Information Systems, 28, 4 (Spring 2012), Aktas, N.; De Bodt, E.; and Van Oppens, H. Legal insider trading and market efficiency. Journal of Banking and Finance, 32, 7 (2008), Allen, F.; Morris, S.; and Shin, H.S. Beauty contests and iterated expectations in asset markets. Review of Financial Studies, 19, 3 (Fall 2006), Bapna, R.; Gupta, A.; Rice, S.; and Sundararajan, A. Trust, reciprocity and the strength of social ties: An online social network based field experiment. Working paper, University of Minnesota, Minneapolis, Beaman, L., and Magruder, J. Who gets the job referral? Evidence from a social networks experiment. American Economic Review, 102, 7 (2012), Calvo-Armengol, A., and Jackson, M.O. The effects of social networks on employment and inequality. American Economic Review, 94, 3 (2004), Carpenter, J.; Kariv, S.; and Schotter, A. Network architecture, cooperation and punishment in public good experiments. Review of Economic Design, 16, 2 3 (2012), Cassar, A., and Rigdon, M. Trust and trustworthiness in networked exchange. Games and Economic Behavior, 71, 2 (2011), Charness, G.; Corominas-Bosch, M.; and Frechette, G.R. Bargaining and network structure: An experiment. Journal of Economic Theory, 136, 1 (2007), Chen, K., and Plott, C. Information aggregation mechanisms: Concept, design and implementation for a sales forecasting problem. Working Paper no. 1131, California Institute of Technology, Pasadena, Cohen, L.; Frazzini, A.; and Malloy, C. The small world of investing: Board connections and mutual fund returns. Journal of Political Economy, 116, 5 (2008), Cohen, L.; Frazzini, A.; and Malloy, C. Sell side school ties. Journal of Finance, 65, 4 (2010),

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25 Prediction Market Accuracy in the Presence of Insider Information Suh, A.; Shin, K.S.; Ahuja, M.; and Kim, M.S. The influence of virtuality on social networks within and across work groups: A multilevel approach. Journal of Management Information Systems, 28, 1 (Summer 2011), Surowiecki, J. The Wisdom of Crowds: Why the Many are Smarter than the Few and How Collective Wisdom Shapes Business, Economies, Societies, and Nations. New York: Doubleday, Tung, Y.A., and Marsden, J.R. Trading volumes with and without private information: A study using computerized market experiments. Journal of Management Information Systems, 17, 1 (Summer 2000), Van Bruggen, G.H.; Spann, M.; Lilien, G.L.; and Skiera, B. Prediction markets as institutional forecasting support systems. Decision Support Systems, 49, 4 (2010), Wolfers, J., and Zitzewitz, E. Prediction markets. Journal of Economic Perspectives, 18, 2 (Spring 2004), Xu, J. Price convexity and skewness. Journal of Finance, 62, 5 (2007), Appendix A: Proof of Proposition 1 Gi v e n t h e a c t i o n profile o f h e r f r i e n d s, participant i s utility is given by ( )= ( ) um, m E a b x m, 2 * i m V cm Ni( g), V i i Ni( g) i ( ) where E V is the expectation with respect to V. The utility function u(m i, m Ni (g)) depends on participant i and her friends effort levels. Let φ(m Ni (g), k i ) be the probability distribution over m Ni (g) induced by Π( k i ). The expected payoff of participant i with degree k i and action m i is equal to ( )= ( )= φ ( ) ( ) U mi, m k E u m m m k um m N ( g) ; i m i, N ( g), N ( g) i i, N ( g), i N i ( g) i i i m Ni ( g) where E mni (g) is the expectation with respect to m Ni (g). We say that a function u exhibits strategic substitutes if an increase in others actions lowers the marginal returns from one s own actions: For all m i > m i and m Ni (g) m Ni (g), um ( i, m u m m um m u m m Ni( g) ) ( i, Ni( g) ) ( i, Ni( g) ) ( i, Ni( g) ). When u exhibits strategic substitutes, a participant s incentive to take a given action decreases as more friends take that action. A participant s utility maximization problem given m i and m Ni (g) is equivalent to a predictor error minimization problem. We can obtain the best mean square predictor of V based on S i : ρv ρε E VS i = V + Si ρ + ρ ρ + ρ ε V 0. ε V Similarly, we can obtain the best mean square predictor of V based on other information sets. If the payoff is a quadratic loss function, then we can show that u(m i, m Ni (g)) exhibits strategic substitutes. If the payoff function exhibits strategic substitutes, then for m i > m i and k i = k i + 1,

26 170 Qiu, Rui, and Whinston U( mi, m k U m m k Ni( g) ; i) ( i, Ni( g) ; i ) = P( k k u m m Ni g i) ( ) ( i, Ni( g) ) um m kn i N g i (, g i ( ) ) ( ) = P k k ( u m m um Ni( g) i) ( i,(, Ni( g) 0) ) i, m kn N g i ( ( g i ( ), 0 ( ) )) = P( k k u m m u Ni( g) i ) ( i,( Ni( g), 0) ) m m kn i N g i (,( g i ( ), 0 ( ) )) P k k ( u m m m Ni( g) i) ( i,(, Ni( g) k + 1) ) ( ) ( i, ( ( ), k N g k + ) i ) N i g 1 um m m = U( m, σ; k ) U( m, σ ; k i ), i i i where the third equality follows from the assumption that friends degrees are all stochastically independent, and the first inequality follows from strategic substitutes. Then, the existence of a symmetric equilibrium follows from the standard existence proof. Let Σ dec be the set of nonincreasing strategies. We can apply the fixed point theorem to the best response correspondence on Σ dec. The correspondence is non-empty, and convex-valued, and it satisfies the standard continuity conditions. Appendix B: Experimental Instructions Experiment Guidelines Th i s is a n e c o n o m i c e x p e r i m e n t, so it is c o n d u c t e d w i t h r e a l m o n e y. Your profit is a direct result of your prediction performance during the experiment. In order to maximize your profits, you need to read the following instructions carefully and use your information wisely. Experiment Description CREC (Central Real Estate Company) needs to predict the size of the rental market, V, in a large metropolitan area. The internal estimation predicted by employees within the company suggests that the market size, V, is probably around $10 million. Figure B1 shows the percent graph of the employees predictions: Most of them think that the market size V = 10. As the head of the marketing department of CREC, you may also consider purchasing an evaluation of the market size from one of several outside experts. If you spend $0.5, the expert will give you a prediction that is twice as accurate as the internal prediction. If you spend $1, the expert will give you a prediction that is four times more accurate than the internal prediction. If you choose to purchase an expert s opinion, you can combine the internal estimation from employees with the expert prediction to get a more precise estimate. Suppose that your prediction is a number x. If you do not purchase expert opinions, your payoff in this round is $5 (x V )²,

27 Prediction Market Accuracy in the Presence of Insider Information 171 Figure B1. The Percent Graph of the Employees Predictions where both x and V are in millions of U.S. dollars. For example, if x = 8, it means you think the market size is $8 million. If you choose to purchase an expert opinion at $0.5, your payoff in this round is $5 (x V )² 0.5. If you choose to purchase an expert opinion at $1, your payoff in this round is $5 (x V )² 1. The more precise your estimate, the higher the payoff you will get. You are free to communicate with other experiment participants on your designated Gmail account. You may have 3, or 2, or 1, or 0 group member(s). You can see them on your designated Gmail account and can discuss with the other group members through Gtalk before making decisions. If your group members purchase evaluations from outside experts, they may provide useful information to you. After reading the guidelines, you need to make a decision on information acquisition: I don t want to purchase an expert s opinion. I want to purchase an expert s opinion with low precision at a cost of $0.50. I want to purchase an expert s opinion with high precision at a cost of $1.00. Then, submit your prediction on the basis of the prior and your signal: