The empirical implications of rank in Bimatrix games

Authors:
Siddharth Barman;Umang Bhaskar;Federico Echenique;Adam Wierman
Affiliations:
California Institute of Technology, Pasadena, CA, USA;California Institute of Technology, Pasadena, CA, USA;California Institute of Technology, Pasadena, CA, USA;California Institute of Technology, Pasadena, CA, USA
Venue:
Proceedings of the fourteenth ACM conference on Electronic commerce
Year:
2013

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Abstract

We study the structural complexity of bimatrix games, formalized via rank, from an empirical perspective. We consider a setting where we have data on player behavior in diverse strategic situations, but where we do not observe the relevant payoff functions. We prove that high complexity (high rank) has empirical consequences when arbitrary data is considered. Additionally, we prove that, in more restrictive classes of data (termed laminar), any observation is rationalizable using a low-rank game: specifically a zero-sum game. Hence complexity as a structural property of a game is not always testable. Finally, we prove a general result connecting the structure of the feasible data sets with the highest rank that may be needed to rationalize a set of observations.