Internet and Network Economics

Volume 4286 of the series Lecture Notes in Computer Science pp 262-273

Sparse Games Are Hard

  • Xi ChenAffiliated withDepartment of Computer Science, Tsinghua University
  • , Xiaotie DengAffiliated withDepartment of Computer Science, City University of Hong Kong
  • , Shang-Hua TengAffiliated withDepartment of Computer Science, Boston University

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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.