1. Outline  Motivation and Modeling Philosophy  Empirical Alternative I: Model of Cognitive Hierarchy (Camerer, Ho, and Chong, QJE, 2004)  Empirical Alternative II: Quantal Response Equilibrium (McKelvey and Palfrey, GEB, 1995)  Empirical Alternative III: Model of Noisy Introspection (Goeree and Holt, AER, 2001)

2. Modeling Principles PrincipleNash CH QRE NI Strategic Thinking     Best Response   Mutual Consistency  

3. Quantal Response Equilibrium Player i choosing strategy j with probability  ij in equilibrium. x ij is i’s expected payoff of choosing j given that others choose their strategy according to equilibrium profile . The values of  depends on.

4. Example 1 q (1-q) p (1-p)

5. Nash Equilibrium q (1-q) p (1-p) 1.1141 q = 0.1238 (1- q)  q = 0.10 1.1141 (1-p) = 1.1141 p  p = 0.5

6. Example 1: =2

7. Prediction as a Function of

8. Example 2

9. QRE Prediction: A = B = 5

10. QRE Prediction: A = B = 100

11. Lieberman’s 2-person Zero-sum Game

12. MLE Estimation

13. Best-fitted QRE Model

14. QRE Plots

15. O’Neill’s 2-person Zero-sum Game

16. QRE and its Special Cases

17. QRE Estimates Across Time

18. QRE Plots

19. Rapoport and Boebel’s 2-person Zero-sum Game

20. QRE Estimates; Experiment I

21. QRE Estimates: Experiment II

22. QRE Estimates Across Time

23. QRE Plots

24. Ochs’s 2-person Non-zero Sum Games

25. QRE Estimates

26. QRE Plots

27. QRE Estimates

28. Prediction

29. QRE Plots

30. QRE versus CH

31. Summary