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The Complexity of Nash Equilibria as Revealed by Data

Barman, Siddharth and Bhaskar, Umang and Echenique, Federico and Wierman, Adam (2014) The Complexity of Nash Equilibria as Revealed by Data. California Institute of Technology , Pasadena, California. (Unpublished)

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In this paper we initiate the study of the computational complexity of Nash equilibria in bimatrix games that are specified via data. This direction is motivated by an attempt to connect the emerging work on the computational complexity of Nash equilibria with the perspective of revealed preference theory, where inputs are data about observed behavior, rather than explicit payoffs. Our results draw such connections for large classes of data sets, and provide a formal basis for studying these connections more generally. In particular, we derive three structural conditions that are sufficient to ensure that a data set is both consistent with Nash equilibria and that the observed equilibria could have been computed effciently: (i) small dimensionality of the observed strategies, (ii) small support size of the observed strategies, and (iii) small chromatic number of the data set. Key to these results is a connection between data sets and the player rank of a game, defined to be the minimum rank of the payoff matrices of the players. We complement our results by constructing data sets that require rationalizing games to have high player rank, which suggests that computational constraints may be important empirically as well.

Item Type:Report or Paper (Working Paper)
Related URLs:
URLURL TypeDescription paper
Echenique, Federico0000-0002-1567-6770
Additional Information:ArXiv: Submitted on 12 Nov 2013 (v1), last revised 26 Sep 2014 (this version, v2)). This research was supported by NSF grants CNS-0846025, EPAS-1307794, and CCF-1101470, along with a Linde/SISL postdoctoral fellowship.
Funding AgencyGrant Number
Linde Institute of Economic and Management ScienceUNSPECIFIED
Caltech Social and Information Sciences LaboratoryUNSPECIFIED
Subject Keywords:Computer Science and Game Theory
Record Number:CaltechAUTHORS:20160321-140122265
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65550
Deposited By: Susan Vite
Deposited On:23 Mar 2016 23:15
Last Modified:09 Jul 2020 22:30

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