The Identification Power of Equilibrium in Simple Games

Joint with: Andres Aradillas-Lopez

The purpose of this paper is to examine the identification power that (Nash) equilibrium assumptions play in learning about parameters in some simple games. In particular, the paper focuses on three static games where we drop the Nash equilibrium assumption and instead use rationalizability (Bernheim (1984) and Pearce (1984)), as the basis for strategic play. The first example examines a bivariate discrete game with complete information of the kind studied in entry models (see Bresnahan and Reiss (1991)). The second example considers the incomplete information version of the discrete bivariate game. Finally, the third example considers a first price auction with independent private values. In each example, we study the inferential question of what can be learned about the parameter of interest using a random sample of observations, under level-k rationality where k is an integer greater or equal to one. As k

increases, our identified set shrinks, limiting to the identified set under full rationality or rationalizability (as k → ∞). This is directly related to the concept of higher order beliefs, which are incorporated into the econometric analysis in our framework. Hence, one is able to categorize what can be learned about the parameters in a model under various maintained levels of rationality. In the process we highlight the role different assumptions play and provide constructive identification results that lead naturally to consistent estimators.

For more information, contact Frank Schorfheide.