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A cognitive hierarchy theory of one-shot games: Some preliminary results

Camerer, Colin F. and Ho, Teck-Hua and Chong, Juin Kuan (2002) A cognitive hierarchy theory of one-shot games: Some preliminary results. . http://resolver.caltech.edu/CaltechAUTHORS:20110204-144123593

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Abstract

Strategic thinking, best-response, and mutual consistency (equilibrium) are three key modelling principles in noncooperative game theory. This paper relaxes mutual consistency to predict how players are likely to behave in in one-shot games before they can learn to equilibrate. We introduce a one-parameter cognitive hierarchy (CH) model to predict behavior in one-shot games, and initial conditions in repeated games. The CH approach assumes that players use k steps of reasoning with frequency f (k). Zero-step players randomize. Players using k (≥ 1) steps best respond given partially rational expectations about what players doing 0 through k - 1 steps actually choose. A simple axiom which expresses the intuition that steps of thinking are increasingly constrained by working memory, implies that f (k) has a Poisson distribution (characterized by a mean number of thinking steps τ ). The CH model converges to dominance-solvable equilibria when τ is large, predicts monotonic entry in binary entry games for τ < 1:25, and predicts effects of group size which are not predicted by Nash equilibrium. Best-fitting values of τ have an interquartile range of (.98,2.40) and a median of 1.65 across 80 experimental samples of matrix games, entry games, mixed-equilibrium games, and dominance-solvable p-beauty contests. The CH model also has economic value because subjects would have raised their earnings substantially if they had best-responded to model forecasts instead of making the choices they did.


Item Type:Report or Paper (Report)
Additional Information:This research was supported by NSF grant SES-0078911. This draft is not intended for publication. It simply summarizes a variety of results in a format accessible to interested readers through web-based archiving. Thanks to C. Mónica Capra, Haitao Cui, Paul Glimcher, and Roger Myerson. Former math nerd Matthew Rabin directed our attention to the golden ratio. Ming Hsu and Brian Rogers provided excellent research assistance. Useful comments were received from seminars at Caltech, Chicago, New York University, Pittsburgh, the Nobel Symposium in Sweden (December 2001), Columbia, and Berkeley.
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Funding AgencyGrant Number
NSFSES-0078911
Record Number:CaltechAUTHORS:20110204-144123593
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20110204-144123593
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:22027
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:16 Sep 2011 22:11
Last Modified:26 Dec 2012 12:54

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