Professor: Andrew B. Whinston McCombs School of Business The University of Texas at Austin

1. Prediction Markets and Business ForecastsOpportunities and Challenges in the New Information Era Professor: Andrew B. Whinston McCombs School of Business The University of Texas at Austin 8/17/2014 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 • Two stocks traded: • REP04: pays $1 per share if Bush 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 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 (http://www.hsx.com) • Movie Stocks • Pays $x per share according to the box office income in the first 4 weeks • Trade opens when the movie starts being planned • Stock price predicts the box office income

5. Other Prediction Markets • Subjects: • Political events • Sports events • Movies incomes • Economic factors • Interest rate • Gasoline price • Inflation rate, etc. • New discoveries in science • Tradesports (http://www.tradesports.com) • Intrade (http://www.intrade.com) • Peddypower (http://www.peddypower.com) • Economic Derivatives (http://www.economicderivatives.com) • NetEchange (http://www.nex.com) • Foresight Exchange (http://www.ideosphere.com/fx/) • etc. Any New Hot Area! Types of Markets 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 • 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 • Fang, Stinchcombe and Whinston (2004) • Putting Your Money where Your Mouth Is • People decide their prediction and how much they want to bet on their prediction. • People will reveal their true prediction • Their bet reveals individual confidence level on the prediction. • 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.

7. A Quick Reminder from Statistics Predicting a random factor X ~ N( 0, s 02) s1 = x + e1 s2 = x + e2 … sn= x + en How should we estimate X ? – Normal Learning Theorem (DeGroot, 1971) • The mean is also an estimator which has the lowest variance among all the linear unbiased estimators (even without normal assumption)

8. c*(t ) cost ci too expensive principal is willing to pay precision ti The Selection Problem How would we decide whether the information is too costly? 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 (siand ti) 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: • suffers private cost to access the information, ci ; • privately knows the precision of their own information source i ; • observes private (independent) signal si only when they pay the costs. • (ci , i ) represents the agent’s ex ante type • Q(c,) denotes the distribution of agents type, and q(c,) is the density; • F() andf() denotes the marginal distribution and density of agent’s precision; • H(c) andh(c) denotes the marginal distribution and density of agent’s costs.

11. Benchmark cases when precision is verifiable -finding optimal c*(t) • The principal sets c*(t) • Agents with precision ti decides whether to participate • Auditable costs: the principal can audit the cost the agents spend and reimburses the agents up to c*au(t). • Non-auditable costs: the principal can not audit the cost hence pays the agents c*non(t) • 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

12. Mathematic treatment Auditable cost: Non-auditable cost:

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

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

15. Betting mechanism design • The principal asks agents to report their own prediction (ri) and to decide how much they want to bet on their prediction (Bi). • Each agent gets rewarded after the state xis observed. The reward functionf = 2Bi1/2 ( a - b(ri-x)2 ) • where a 0, b  0, are parameters set by the firm. • Each agent’s optimal strategy (ri*(si, i), Bi*(si, i) ) is derived by solving the following problem

16. Proposition: (optimal strategy)

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

18. Proposition: (participation) People will participate when their cost of acquiring the signal is lower than the gain from the betting market. • Proposition: (optimal parameters) • When p > 0, b*  a* > 0 when h(c) is continuous and h(0) >0 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. • 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 loss of efficiency is the largest when • Possible ex post Inefficiency: • the principal may regret setting a parameter too high or too low after observing the agents’ participation. • Example: two extreme cases of

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

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

22. Q&A T h a n k Y o u !