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Testing Iterative Dominance in Centipede Game: Experimental Insights from Caltech

This study investigates the iterative dominance principle in a Centipede game experiment conducted with participants from the Caltech Board of Trustees and other subject pools. By analyzing both finite and infinite threshold variants, we explore factors such as altruistic behavior, group size, and the impact of experience on decision-making. Results indicate convergence toward equilibrium over time, with noteworthy differences in choices between inexperienced and experienced subjects. Our findings provide valuable insights into strategic interactions in constant-sum games.

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Testing Iterative Dominance in Centipede Game: Experimental Insights from Caltech

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  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 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 • David Baltimore President California Institute of Technology • Donald L. Bren Chairman of the BoardThe Irvine Company • Eli BroadChairmanSunAmerica Inc. • Lounette M. Dyer Chairman Silk Route Technology

  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 Bin 1 Bin 0 x 100

  28. Infinite-Threshold pBC

  29. Maximum Likelihood Estimates

  30. Further Analysis on Iterated Best-Response

  31. Special Cases • Cournot Best Response (R=1, b1 = 1.0) • Fictitious Play (bs= 1/R) • Weighted Fictitious Play (bs=bs)

  32. Maximum Likelihood Estimates

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