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

Abstract

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

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