1. Outline  In-Class Experiment on Centipede Game  Test of Iterative Dominance Principle I: McKelvey and Palfrey (1992)  Test of Iterative Dominance Principle II: Ho, Camerer, and Weigelt (1988)

2. Motivation  Constant-sum games  Control for altruistic behavior  Does experience matter?  Finite-threshold versus infinite-threshold  Allow violations of higher level of iterated dominance  Group size and learning

3. Finite-Threshold p-BC

4. Infinite-Threshold pBC

5. Experimental Design

6. pBC Contest  Every player simultaneously chooses a number from 0 to 100  Compute the group average  Define Target Number to be 0.7 times the group average  The winner is the player whose number is the closet to the Target Number  The prize to the winner is US$10 + $1 x Number of Participant

7. A Sample of Caltech Board of Trustees David Baltimore President California Institute of Technology Donald L. Bren Chairman of the Board The Irvine Company Eli Broad Chairman SunAmerica Inc. Lounette M. Dyer Chairman Silk Route Technology David D. Ho Director The Aaron Diamond AIDS Research Center Gordon E. Moore Chairman Emeritus Intel Corporation Stephen A. Ross Co-Chairman, Roll and Ross Asset Mgt Corp Sally K. Ride President Imaginary Lines, Inc., and Hibben Professor of Physics

8. Results from Caltech Board of Trustees

9. Results from Two Other Smart Subject Pools

10. Results from College Students

11. Results from FT, Spektrum Readers

12. Basic Results

13. Finite-Threshold p-BC

14. Infinite-Threshold pBC

15. Infinite-Threshold Games (Inexperienced Subjects, p=0.7, n=7)

16. Infinite-Threshold Games, (Experienced Subjects, p=0.7, n=7)

17. Infinite-Threshold Games (Inexperienced Subjects, p=0.9, n=7)

18. Infinite-Threshold Games (Experienced Subjects, p=0.9, n=7)

19. Infinite-Threshold Games (Inexperienced Subjects, p=0.7, n=3)

20. Infinite-Threshold Games (Experienced Subjects, p=0.7, n=3)

21. Infinite-Threshold Games (Inexperienced Subjects, p=0.9, n=3)

22. Infinite-Threshold Games (Experienced Subjects, p=0.9, n=3)

23. Finite-Threshold Games, n=3

24. Finite-Threshold Games, n=7

25. Summary of Basic Results  Result 1: First-period choices are far from equilibrium. Choice converge towards equilibrium point over time.  Result 2: On average, choices are closer to the equilibrium point for games with finite thresholds, and for games with p farther from 1.  Result 3: Choices are closer to equilibrium for large (7- person) groups than for small (3-person) groups  Result 4: Choices by experienced subjects are no different than choices by inexperienced subjects in the first round, but converge faster to equilibrium.

26. Further Analysis on Iterated Dominance

27. Assignment of Type in Bin b 100 Bin 0 Bin 1 x

28. Infinite-Threshold pBC

29. Maximum Likelihood Estimates

30. Further Analysis on Iterated Best- Response

31. Special Cases  Cournot Best Response (R=1,   = 1.0)  Fictitious Play (  s = 1/R)  Weighted Fictitious Play (  s =  s )

32. Maximum Likelihood Estimates