A cognitive hierarchy model of games

Creators: Camerer, Colin F.; Ho, Teck-Hua; Chong, Juin-Kuan

Abstract

Players in a game are "in equilibrium" if they are rational, and accurately predict other players' strategies. In many experiments, however, players are not in equilibrium. An alternative is "cognitive hierarchy" (CH) theory, where each player assumes that his strategy is the most sophisticated. The CH model has inductively defined strategic categories: step 0 players randomize; and step k thinkers best-respond, assuming that other players are distributed over step 0 through step k − 1. This model fits empirical data, and explains why equilibrium theory predicts behavior well in some games and poorly in others. An average of 1.5 steps fits data from many games.

Additional Information

© 2004 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Posted Online March 13, 2006. This research was supported by NSF grants SES-0078911 and SES-0078853. Thanks to C. Mónica Capra, Haitao Cui, Paul Glimcher, and Roger Myerson. Sara Robinson was a helpful wordsmith. Former math nerd Matthew Rabin directed our attention to the golden ratio. Meghana Bhatt, Ming Hsu, Ye Li, Brian Rogers, and Lisa Wang provided excellent research assistance. Useful comments were received from seminars at University of California at Berkeley, California Institute of Technology, University of Chicago, Carnegie Mellon University, Columbia University, Harvard University, New York University, University of Pittsburgh, Stanford University, the Nobel Symposium in Sweden (December 2001), and from four referees and an unusually helpful editor (Edward Glaeser).

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