Prediction Markets and Business Forecasts Opportunities and Challenges in the New Information Era Professor: Andrew B. Whinston McCombs School of Business The University of Texas at Austin 10/9/2015 Reference: Fan, Srinivasan, Stallaert and Whinston, “Electronic Commerce and the Revolution in Financial Markets”, Published by Thomson Learning, 2002.

2 A New Way of Making Predictions 2004 Presidential Election Winner Takes All Market 2004 Presidential Election Winner Takes All Market Two stocks traded: Two stocks traded: REP04: pays $1 per share if Bush wins, $0 if he loses REP04: pays $1 per share if Bush wins, $0 if he loses DEM04: pays $1 per share if Kerry wins, $0 if he loses DEM04: pays $1 per share if Kerry wins, $0 if he loses Before Dec 5, 2004, people can freely buy and sell the stocks, just like the real stock market Before Dec 5, 2004, people can freely buy and sell the stocks, just like the real stock market The Prices of the stocks: double auction mechanism just like the real stock market

3 The market price reveals the candidate’s chances of winning

4 Hollywood Stock Exchange ( Movie Stocks Movie Stocks Pays $x per share according to the box office income in the first 4 weeks Pays $x per share according to the box office income in the first 4 weeks Trade opens when the movie starts being planned Trade opens when the movie starts being planned Stock price predicts the box office income Stock price predicts the box office income

5 Types of Markets Other Prediction Markets  Tradesports (  Intrade (  Peddypower (  Economic Derivatives (  NetEchange (  Foresight Exchange (  etc. Subjects: Subjects: Political events Political events Sports events Sports events Movies incomes Movies incomes Economic factors Economic factors Interest rate Interest rate Gasoline price Gasoline price Inflation rate, etc. Inflation rate, etc. New discoveries in science New discoveries in science Any New Hot Area! Double Auction (stock market) Parimutuel Pricing (betting market) One Side Auction (auction market)

6 New Era of Business Forecasting Implementation of the market mechanisms into the Decision Support System Implementation of the market mechanisms into the Decision Support System flexibility to integrate new aspects and subjective knowledge in the prediction (e.g., a competitor’s unconventional move.) flexibility to integrate new aspects and subjective knowledge in the prediction (e.g., a competitor’s unconventional move.) quantifiable incentives for people to tell the truth quantifiable incentives for people to tell the truth Fang, Stinchcombe and Whinston (2004) Fang, Stinchcombe and Whinston (2004) Putting Your Money where Your Mouth Is Putting Your Money where Your Mouth Is People decide their prediction and how much they want to bet on their prediction. People decide their prediction and how much they want to bet on their prediction. People will reveal their true prediction People will reveal their true prediction Their bet reveals individual confidence level on the prediction. Their bet reveals individual confidence level on the prediction. Weights are assigned to individual predictions based on agents’ bets. Weights are assigned to individual predictions based on agents’ bets. Each person can expect to gain if their information is valuable. The gain increases as the quality of information, which encourage them to learn. Each person can expect to gain if their information is valuable. The gain increases as the quality of information, which encourage them to learn.

7 A Quick Reminder from Statistics s 1 = x +  1 s 2 = x +  2 … s n = x +  n How should we estimate X ? The mean is also an estimator which has the lowest variance among all the linear unbiased estimators (even without normal assumption) The mean is also an estimator which has the lowest variance among all the linear unbiased estimators (even without normal assumption) – Normal Learning Theorem (DeGroot, 1971) Predicting a random factor X ~ N( 0,  0 2 )

8 The Selection Problem How would we decide whether the information is too costly? cost c i precision  i too expensive c*(  ) principal is willing to pay The cutoff is expected to be an increasing function

9 Selection Problem -- Model A risk neutral firm (the principal) wants to predict a random future state X ~N (0,1) If all the agents in the set S share the information ( s i and   ) truthfully with the principal, the “best estimator ” is derived from the following maximization problem. -- a weighted average of signals

10 The agents N potential risk-neutral agents, each: N potential risk-neutral agents, each: suffers private cost to access the information, c i ; suffers private cost to access the information, c i ; privately knows the precision of their own information source  i ; privately knows the precision of their own information source  i ; observes private (independent) signal s i only when they pay the costs. observes private (independent) signal s i only when they pay the costs. (c i,  i ) represents the agent’s ex ante type (c i,  i ) represents the agent’s ex ante type Q(c,  ) denotes the distribution of agents type, and q(c,  ) is the density; Q(c,  ) denotes the distribution of agents type, and q(c,  ) is the density; F(  ) and f(  ) denotes the marginal distribution and density of agent’s precision; F(  ) and f(  ) denotes the marginal distribution and density of agent’s precision; H(c) and h(c) denotes the marginal distribution and density of agent’s costs. H(c) and h(c) denotes the marginal distribution and density of agent’s costs.

11 Benchmark cases when precision is verifiable -finding optimal c*(  ) The principal sets c*(  ) The principal sets c*(  ) Agents with precision  i decides whether to participate Agents with precision  i decides whether to participate Auditable costs: the principal can audit the cost the agents spend and reimburses the agents up to c* au (  ). Auditable costs: the principal can audit the cost the agents spend and reimburses the agents up to c* au (  ). Non-auditable costs: the principal can not audit the cost hence pays the agents c* non (  ) Non-auditable costs: the principal can not audit the cost hence pays the agents c* non (  ) Inside the firm: the principal needs to take into account the fact that the agents consumes resources inside the firm to get the prediction. Inside the firm: the principal needs to take into account the fact that the agents consumes resources inside the firm to get the prediction. The set of agents who will participate The set of agents who will participate

12 Mathematic treatment Auditable cost:Non-auditable cost:

13 Results of Existence and Monotonicity Assumptions: Assumptions: The density q is greater than 0 on a set of the form for some non-decreasing function and some The density q is greater than 0 on a set of the form for some non-decreasing function and some Proposition: Proposition: In both cases, we can find the optimal c* maximizes the principal’s payoff; moreover, c* is non-decreasing. In both cases, we can find the optimal c* maximizes the principal’s payoff; moreover, c* is non-decreasing.

14 Result (cont) Non-auditable case: c* will always satisfy c* will always satisfy c*(  ) has to be zero even as long as there exists some agent with precision . Auditable case: c*(  )  c* is set so that no agent with strictly positive cost will be selected. c*(  ) need not be zero if the principal believes that there is no agent with precision  and strictly positive cost. Generally speaking, we can get that c* goes to zero when the number of agents goes to infinity.

15 Betting mechanism design The principal asks agents to report their own prediction ( r i ) and to decide how much they want to bet on their prediction ( B i ). The principal asks agents to report their own prediction ( r i ) and to decide how much they want to bet on their prediction ( B i ). Each agent gets rewarded after the state x is observed. The reward function f = 2B i 1/2 ( a - b(r i -x) 2 ) Each agent gets rewarded after the state x is observed. The reward function f = 2B i 1/2 ( a - b(r i -x) 2 ) where a  0, b  0, are parameters set by the firm. where a  0, b  0, are parameters set by the firm. Each agent ’ s optimal strategy ( r i * ( s i,  i ), B i * ( s i,  i ) ) is derived by solving the following problem Each agent ’ s optimal strategy ( r i * ( s i,  i ), B i * ( s i,  i ) ) is derived by solving the following problem

16 Proposition: (optimal strategy) Proposition: (optimal strategy)

17 Revelation Corollary: (revealing) Corollary: (revealing) The signal and precision are reflected through the bet and report.

18 Proposition: (participation) Proposition: (participation) Proposition: (optimal parameters) Proposition: (optimal parameters) When p > 0, b *  a * > 0 when h(c) is continuous and h(0) >0 When p > 0, b *  a * > 0 when h(c) is continuous and h(0) >0 People will participate when their cost of acquiring the signal is lower than the gain from the betting market. The optimal reward function always exists. It varies when the principal’s perceived distribution functions of cost and precision change.

19 Discussion of Simultaneous Betting Market Repeated Betting due to anonymity. Repeated Betting due to anonymity. If an agent can acquire two identities and bet twice, she will repeat the optimal strategy twice and get twice as much her expected payoff. If an agent can acquire two identities and bet twice, she will repeat the optimal strategy twice and get twice as much her expected payoff. The predictor is less efficient (i.e. variance is larger) The predictor is less efficient (i.e. variance is larger) The loss of efficiency is the largest when The loss of efficiency is the largest when Possible ex post Inefficiency: Possible ex post Inefficiency: the principal may regret setting a parameter too high or too low after observing the agents’ participation. the principal may regret setting a parameter too high or too low after observing the agents’ participation. Example: two extreme cases of Example: two extreme cases of

20Dynamics Principal’s trade-off: whether should I stop learning now? Principal’s trade-off: whether should I stop learning now? To generate forecast earlier (time discount) To generate forecast earlier (time discount) Pay more, improve forecast, but decide late Pay more, improve forecast, but decide late Dynamic Programming: Dynamic Programming: Optimal Stopping Time Intuition: ability to adjust the parameter according to how information is incorporated

21 Extension Extension: auctions market Extension: auctions market Implications to the new organization forms Implications to the new organization forms

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