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

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

A cognitive hierarchy model of games

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

On the Public Economics of Casino Gambling

This paper studies casino-style gambling from the public economics point of view in a jurisdiction populated by oligopolistically competitive legal casinos. We consider three different regimes: laissez-faire, entry regulation and tax regulation. The model highlights three important external effects from casino-style gambling: non-casino income creation, social disorder costs, and casino exporting to other jurisdictions. In the generalized case with an endogenously-determined ratio of local to total gamblers, we allow the configuration of casinos to be centralized or jurisdiction-wide dispersed. A complete comparison between equilibrium and command optimum outcomes is provided, and the welfare consequences under the three regimes and two casino configurations are examined.Casino gambling, externalities, oligopoly pricing, entry, tax regulation

Working Hours Reduction and Endogenous Growth

This paper formulates an endogenous growth model and uses it to inquire into the long-run impact of work-sharing arrangements on economic growth. We show that the styles of wage contract, namely salary-style and hourly-style contracts, are a key factor in determining the long-run growth effects of working time reduction. If the labor market is overwhelmingly salaried arrangement, then the extent of wage flexibility is relatively low; as a consequence, a policy of reducing working hours will deteriorate economic growth. On the contrary, if hourly pay predominates, then the wage system tends to increase the degree of wage flexibility. Thus, a cut in working time may favor the economy’s growth rate.Working hours reduction, Endogenous growth