Information, Control and Games

1. Information, Control and Games Shi-Chung Chang EE-II 245, Tel: 2363-5251 ext. 245 scchang@cc.ee.ntu.edu.tw, http://recipe.ee.ntu.edu.tw/scc.htm Office Hours: Mon/Wed 1:00-2:00 pm or by appointment Yi-Nung Yang (03 ) 2655201 ext. 5205, yinung@cycu.edu.tw

2. Introduction to Experimental Games Experimental Evidence on Games and Anomaly

3. Environments, Institution, and Behavior

4. Environments, Institution • Environment • agent • with preference, risk attitude, knowledge (learning behavior), skill, endowment, cost structure, ... • resources • commodities, inputs • Institution • rules of transaction/exchange(incentive, i.e., reward/punishment) • rules of communication (information transmission/cost) • contract (property right)

5. Reasons for conducting experiments • Test a theory, or discriminate between theories • 荷式、英式拍賣, double-auction, post-offer auction • Explore the causes of a theory’s failure • real data 可能包含太多變因, e.g., ultimatum game • Establish empirical regularities as a basis for new theory • 利用實驗結果建立新理論, 或可解決問題的模型, e.g., emission permit, airport slot • Compare environments • 不同偏好 (效用, 風險, 公平正義認知), 不同知識 • Compare institutions • 比較不同之交易制度, 資訊傳遞... • Evaluate policy proposals • The laboratory as a testing ground for institutional design

6. A Note on the Design of Experiments • Benchmark (對照組, 或理論值) • Treatment • environment • institutione.g., 學習效果, 資訊傳遞, 交易制度, 動機設計, 風險態度 • Joint hypothesis • randomness/anonymity of players • information necessary to the Subjects • Tools of analyzing observations in the Lab. • percentage/distribution • ANOVA/MANOVA • econometric model

7. Experiments of Competitive Market Behavior • By Vernon L. Smith (1962, JPE) • Competitive Market • 買賣雙方人數眾多 (皆為 price taker) • 價格機能:供不應求, 則價漲; 供過於求, 則價跌 • 市場愈敏感 (供需曲線愈平緩), 則收歛愈快 • Design of the Experiment • The subjects are randomly assigned to buyer/supplier with privately given Value and Cost of one-unit (virtual) good. • Incentive: maxmizing V-P and P-C (no monetary rewards) • Information transmission: Verbal offer/acceptance • Information history: observable • Transaction: Double-Auction

8. Benchmark

9. Sensitivity of Demand/Supply (flat curves)

10. Sensitivity of Demand/Supply (steep curves)

11. A Parallel Shift in Demand with Horizontal Supply

12. A Changed Slope in Demand

13. A decrease in demand A Decrease in Demand with Vertical Supply

14. A Change in Market Organization Buyers and Sellers bidding Sellers only bidding

15. Summary of Smith’s (1962) findings • Small numbers of buyers/sellers can achieve competitive equilibrium (as long as prohibited collusion with publicity of all bids • Competitive equilibrium works in changes in demand except overshooting • When supply curve is perfectly elastic (horizontal line), empirical equilibrium > theoretical equilibrium • Seller-only market exhibits weaker tendencies toward equilibrium

16. Matching Pennies • Previous Matching Pennies Game and Best Response f()

17. Modified Matching Pennies Game • If Payoff of player 1 on {B,B} is raised to 320 !!!!!

18. Modified Matching Pennies Game • Payoff of player 1 on {B,B} is raised to 320 !!!!!

19. Modified Matching Pennies Game • Best Response f() of modified matching pennies game • Mixed strategy equil. (1, 2) = ({1/2,1/2},{1/8,7/8})

20. Experimental Design of Matching Pennies • Goeree and Holt (2001, AER) • 50 subjects in a one-shot game • Subjects were randomly matched and assigned row or column players. • Repeated games were investigated and the results were persistent

21. Experimental Evidence on Matching Pennies • Goeree and Holt (2001, AER)

22. (84%) (96%) The BoS game: A coordination game • A typical coordination game 0, • A modified version with an option S: when x = 0 • What are the Nash equil. ? • “S” is to be eliminated • (L,L) and (H, H) and a mixed strategy(1, 2) = ({1/3, 2/3}, {1/3, 2/3}) • Experimental Evidence

23. (76%) 400, (64%) The BoS game: A coordination game • When x = 400 • What are the Nash equil. ? • (L,L) and (H, H) • With this change (x =0 to x=400) • Player 1’s choice on H reduces from 96% to 64% whilePlayer 2’s choice on L also reduces from 84% to 76%. • When x =0 , coordination on (H,H) is 80%When x =400 , coordination on (H,H) drops to 32%

24. The Ultimatum Game (最後通牒賽局) • Distribution Game • Two player to split $ c • Player 1 offers player 2 $x (up to $c) • if player 2 accept this amount, the payoffs are (c-x, x)if player 2 reject, the payoffs are (0,0) • Subgame Perfect Equilibrium? • min. increnment = 0.01

25. Experiments on the Ultimatum Game • 1970s in Germany (GSS,1982) in textbook • Players • 42 graduate students of economics • split into 2 groups and seated on different sides of a room • Player 1 wrote down x on a formThis form was then given to a randomly determined player 2 • Payoff:c  (4 , 10) DM (2~5 USD)minimum increment 1 cent (0.01 DM) • Each player had 10 min. to make her decision • The entire game was repeated a week later.

26. Experimental Results (GSS,1982) • Mean of x is not close to 0.01 DM

27. (買賣) (分配) Experimental Evidence on the Ultimatum Game • Hoffman (1994) cited by Smith (2002)

28. Trust Game • A simple two-stage game • Trust the other player? Go on next step could get more! • What is the Subgame Perfect Eqiilibrium?

29. Experimental Evidence on Trust Game

30. Experimental Evidence on Trust Game

31. 3-stage Trust Game SPE payoffs

32. Voluntary vs Involuntary Trust Game

33. Robustness in the Trust Game • By Goeree and Holt (2001, AER) • randomly paired 50 subjects who play this game only once • Treatment • Robustness of the backward induction

34. Robustness in the Trust Game: A benchmark

35. Robustness in the Trust Game: A Treatment • The cost of irrationality is small?

36. Incredible Threat ? • That 1st player chooses R signals a “win-win” message • That 1st player chooses R signals a “selfish” message?

37. Incredible Threat: A Treatment

38. Incredible Threat after Many Rounds Cooperation payoffs SPE payoffs

39. What we have learned from Experiments? • Institutions matters • posted offer pricing converges more slowly and erratically and is less than continuous double auction • Unconscious optimization in market interactions • learning by doing • Information: less can be better • Incomplete or asymmetric info. often leads to sub-optimum • Common information is not sufficient to yield common expectations or “knowledge” • you are not sure others how to use the common info.

40. What we have learned from Experiments? • Dominated strategies are for playing, not for eliminating • Dominant strategies should only occur in the common knowledge • Efficiency and under-revelation are compatible • auction game • The endowment effect • willingness to pay  willingness to accept • Fairness: Taste or Expectation? • The ultimatum game: A monopoly can extract all surplus of consumers?

41. Application of Experimental Games • Auction designs • Deregulation of Airline Route • Electricity Market • Iowa Electronic (Futures) Market