May (Revised July) 2010
Behavioral game theory experiments consistently reveal that individuals deviate from theoretically optimal (Nash equilibrium) strategies even in simple games. The alpha-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.
Several authors, beginning with the works of Stahl and Wilson (1995, 1994) and Nagel (1995), have proposed an intuitively appealing and formally elegant cognitive hierarchy (CH) model of strategic reasoning for these instances where Nash equilibrium is patently unrealistic. In a CH model the player population is partitioned according to how many steps of iterated reasoning players perform when strategizing and each subpopulation plays conditionally optimally according to their level of strategic foresight. In this paper we specifically conside two common instantiations of the general CH model, the CH-Poisson model of Camerer et al. (2004) and the level-k model as described in Crawford and Iriberri (2007), evaluating how well each succeeds at describing empirical beauty contest data.
Our evaluation proceeds by first developing a highly flexible semiparametric CH model which includes these two commonly studied models as special cases. We then 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.
The key finding is that while the CH-Poisson and the level-k models do not describe our new data well, the more general semiparametric CH model significantly outperforms a non-CH alternative model, lending support to the possibility that a cognitive hierarchy strategic structure underpins the observed bids.
Keywords: behavioral game theory, cognitive hierarchy models, model assessment, bounded rationality.
The manuscript is available in PDF format.