Equilibrium Play and Adaptive Learning in a Three-Person Centipede Game

The two-person centipede game is one of the most celebrated paradoxes of backward induction in complete information extensive form games. An experimental investigation of a three-person centipede game shows that the paradoxical results are strongly affected by the size of the stakes. When the number of players in the game is increased from two to three and the game is played for unusually high stakes with group composition being randomly changed from trial to trial, the paradox is considerably weakened as players approach equilibrium play with multiple iterations of the stage game. When the game is played with low stakes, there is no evidence for equilibrium play or learning across iterations of the stage game. An adaptive learning model that assumes updating of the individual probabilities of choice outperforms alternative static and dynamic models in accounting for the major results observed in the high-stake experiment.

[1]  K. Binmore.  A note on backward induction , 1996 .

[2]  K. Binmore,et al.  Does Minimax Work? An Experimental Study , 2001 .

[3]  Colin Camerer,et al.  The Effects of Financial Incentives in Experiments: A Review and Capital-Labor-Production Framework , 1999 .

[4]  Dilip Mookherjee,et al.  Learning behavior in an experimental matching pennies game , 1994 .

[5]  D. Fudenberg,et al.  Consistency and Cautious Fictitious Play , 1995 .

[6]  A. Roth,et al.  Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria , 1998 .

[7]  Klaus G. Zauner.  A Payoff Uncertainty Explanation of Results in Experimental Centipede Games , 1999 .

[8]  Teck-Hua Ho,et al.  Experience-Weighted Attraction Learning in Games: A Unifying Approach , 1997 .

[9]  R. McKelvey,et al.  Quantal Response Equilibria for Extensive Form Games , 1998 .

[10]  R. McKelvey,et al.  An experimental study of the centipede game , 1992 .

[11]  Ken Binmore,et al.  Modeling rational players I , 1987 .

[12]  J. Harsanyi.  Games with randomly disturbed payoffs: A new rationale for mixed-strategy equilibrium points , 1973 .

[13]  Colin Camerer,et al.  Behavioral Game Theory: Thinking, Learning and Teaching , 2001 .

[14]  Teck-Hua Ho,et al.  Trust Building Among Strangers , 2005, Manag. Sci..

[15]  Nagel,et al.  Experimental Results on the Centipede Game in Normal Form: An Investigation on Learning. , 1998, Journal of mathematical psychology.

[16]  R. Aumann.  On the Centipede Game , 1998 .

[17]  R. McKelvey,et al.  An experimental study of constant-sum centipede games , 1996 .

[18]  Farshid Vahid,et al.  Predicting How People Play Games: A Simple Dynamic Model of Choice , 2001, Games Econ. Behav..

[19]  Dale O. Stahl,et al.  Rule Learning in Symmetric Normal-Form Games: Theory and Evidence , 2000, Games Econ. Behav..

[20]  R. Aumann.  Backward induction and common knowledge of rationality , 1995 .

[21]  Colin Camerer,et al.  Experience‐weighted Attraction Learning in Normal Form Games , 1999 .

[22]  Dale O. Stahl,et al.  Evidence based rules and learning in symmetric normal-form games , 1999, Int. J. Game Theory.

[23]  A. Rapoport,et al.  Prisoner's Dilemma: A Study in Conflict and Co-operation , 1970 .

[24]  Giovanni Ponti,et al.  Cycles of Learning in the Centipede Game , 2000, Games Econ. Behav..

[25]  R. Aumann.  Correlated Equilibrium as an Expression of Bayesian Rationality Author ( s ) , 1987 .

[26]  Nick Feltovich,et al.  Reinforcement-based vs. Belief-based Learning Models in Experimental Asymmetric-information Games , 2000 .

[27]  R. Hertwig,et al.  Experimental practices in economics: A methodological challenge for psychologists? , 2001, Behavioral and Brain Sciences.

[28]  Colin F. Camerer,et al.  Experience-Weighted Attraction Learning in Sender-Receiver Signaling Games , 2001 .

[29]  Colin F. Camerer,et al.  Experience-weighted attraction learning in sender-receiver signaling games , 2000 .

[30]  Robert J. Aumann,et al.  Reply to Binmore , 1996 .

[31]  Partha Dasgupta,et al.  Economic Analysis of Markets and Games: Essays in Honor of Frank Hahn , 1992 .

[32]  R. Rosenthal.  Games of perfect information, predatory pricing and the chain-store paradox , 1981 .

[33]  Y. Htun.  Irrationality in Game Theory , 2005 .

[34]  A. B. Markman,et al.  Choice output and choice processing: An analogy to similarity , 2001, Behavioral and Brain Sciences.

[35]  A. Roth,et al.  Learning in Extensive-Form Games: Experimental Data and Simple Dynamic Models in the Intermediate Term* , 1995 .

[36]  Dilip Mookherjee,et al.  Learning and Decision Costs in Experimental Constant Sum Games , 1997 .

[37]  D. Fudenberg,et al.  The Theory of Learning in Games , 1998 .