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The Empirical Implications of Rank in Bimatrix Games

Barman, Siddharth and Bhaskar, Umang and Echenique, Federico and Wierman, Adam (2013) The Empirical Implications of Rank in Bimatrix Games. In: EC '13 Proceedings of the fourteenth ACM conference on Electronic commerce. ACM , New York, NY, pp. 55-72. ISBN 978-1-4503-1962-1 . https://resolver.caltech.edu/CaltechAUTHORS:20131008-155108539

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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.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1145/2492002.2482589DOIArticle
https://arxiv.org/abs/1305.3336arXivDiscussion Paper
ORCID:
AuthorORCID
Echenique, Federico0000-0002-1567-6770
Additional Information:Copyright ©2013 ACM. This research was supported by NSF grants CNS-0846025 and CCF-1101470.
Funders:
Funding AgencyGrant Number
NSFCNS-0846025
NSFCCF-1101470
Subject Keywords:Theory, Algorithms, Economics, Game Theory; Nash Equilibrium; Revealed Preference; Matrix Rank
Classification Code:F.2.0 [Analysis of Algorithms and Problem Complexity]:General
Record Number:CaltechAUTHORS:20131008-155108539
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20131008-155108539
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:41760
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:08 Oct 2013 23:02
Last Modified:03 Oct 2019 05:51

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