Behavioral game theory experiments consistently reveal that individuals deviate from theoretically optimal (Nash equilibrium) strategies even in simple games. The α-beauty contest is among the simplest games that elicit such non-optimal behavior; accordingly, there is substantial interest in formally characterizing the observed play for this game. Contributing to such an effort, and building on earlier work by Stahl and Wilson (1995, 1994) and Nagel (1995), Camerer et al. (2004) introduce an intuitively appealing and formally elegant cognitive hierarchy (CH) model of strategic reasoning. Under their model the player population is partitioned according to a Poisson distribution (CH-P) and the resulting subgroups are hierarchically ordered in terms of how many steps of iterated reasoning they perform when strategizing. Though the analytic properties of this model provide easily interpretable parameters, we are able to show that the data do not strongly support such a model, at least in the case of the α-beauty contest. In fact, we find no evidence of cognitive hierarchy structure at all. We arrive at this result by developing a rigorous testing methodology consisting of three key components. First, we generalize CH-P by developing a flexible semiparametric (SP) CH model which nests many common CH variants. Second, we describe an experiment to collect data specifically tailored to test key assumptions of the CH framework. Finally, we describe an appropriate null model against which to evaluate the ability of CH models to characterize our experimental data. Some key words: behavioral game theory, cognitive hierarchy models, model assessment, bounded rationality. 2 1

Abstract not found

How can a rational player strategically control a myopic best reply player in a repeated two-player game? We show that in games with strategic substitutes or strategic complements the optimal control strategy is monotone in the initial action of the opponent and across time periods. As an interesting example outside this class of games we present a Cournot duopoly with non-negative prices and show that in a finite repetition the optimal control strategy involves a cycle.