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. Four-move Centipede Game

3. Six-move Centipede Game

5. Variables and Predictions  Proportion of Observations at each Terminal Node, f j, (j=1-5 for four-move and j=1-7 for six-move games)  Implied Take Probability at Each Stage, p j (j=1-4 for four-move and j=1-6 for six move games)  Iterative Dominance Predictions  f j = 1.0 for j=1 and 0 otherwise  p j = 1.0 for all j.

6. Experimental Design

7. Basic Results: f j

8. Basic Results: p j

9. Basic Results: Cumulative Outcome Frequencies

10. Basic Results: Early versus Later Rounds

11. Summary of Basic Results  All outcomes occur with strictly positive probability.  p j is higher at higher j.  Behaviors become “more rational” in later rounds.  p j is higher in 4-move game than in 6-move game for the same j.  For a given j, p n-j in a n-move game increases with n.  There are 9 players who chose PASS at every opportunity.

12. Basic Model  “Gang of Four” (Kreps, Milgrom, Roberts, and Wilson, JET, 1982) Story  Complete  Incomplete information game where the prob. of a selfish individual equals q and the prob. of an altruist is 1-q. This is common knowledge.  Selfish individuals have an incentive to “mimic” the altruists by choosing to PASS in the earlier stages.

13. Properties of Prediction  For any q, Blue chooses TAKE with probability 1 on its last move.  If 1-q > 1/7, both Red and Blue always choose PASS, except on the last move, when Blue chooses TAKE.  If 0 < 1-q < 1/7, the equilibrium involves mixed strategies.  If q=1, then both Red and Blue always choose TAKE.  For 1-q> 1/49 in the 4-move game and 1-q > 1/243, the solution satisfies p i > p j whenever i > j.

14. Proportions of Outcomes as a Function of the Level of Altruism

16. Problems and Solutions  For any 1-q, there is at least one outcome with 0 or close to 0 probability of occurrence.  Possibility of error in actions  TAKE with probability (1-  t ) p* and makes a random move (50-50 chance of PASS and TAKE) with probability  t.  Learning:  Heterogeneity in beliefs (errors in beliefs)  Q (true) versus q i (drawn from beta distribution (  ))  Each player plays the game as if it were common knowledge that the opponent had the same belief.

17. Equilibrium with Errors in Actions

19. The Likelihood Function  A player draws a belief q  For every t and every  t, and for each of the player’s decision nodes, v, we have the equilibrium prob. of TAKE given by:  Player i’s prob. of choosing TAKE given q:

20. The Likelihood Function  If Q is the true proportion for the fraction of selfish players, then the likelihood becomes:  The Likelihood function is:

21. Maximum Likelihood Estimates

22. Estimated Distribution of Beliefs

23. Tests of Nested Models

24. Differences in Noisy Actions Across Treatments

25. Predicted Versus Actual Choices

26. Predicted versus Actual Choices

27. Summary