Sparse games are hard

Authors:
Xi Chen;Xiaotie Deng;Shang-Hua Teng
Affiliations:
Department of Computer Science, Tsinghua University, Beijing;Department of Computer Science, City University of Hong Kong, Hong Kong;Department of Computer Science, Boston University, Boston
Venue:
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Year:
2006

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Abstract

A two-player game is sparse if most of its payoff entries are zeros. We show that the problem of computing a Nash equilibrium remains PPAD-hard to approximate in fully polynomial time for sparse games. On the algorithmic side, we give a simple and polynomial-time algorithm for finding exact Nash equilibria in a class of sparse win-lose games.