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Hard-to-Solve Bimatrix Games

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  • Rahul Savani
  • Bernhard Stengel

Abstract

The Lemke-Howson algorithm is the classical method for finding one Nash equilibrium of a bimatrix game. This paper presents a class of square bimatrix games for which this algorithm takes, even in the best case, an exponential number of steps in the dimension d of the game. Using polytope theory, the games are constructed using pairs of dual cyclic polytopes with 2d suitably labeled facets in d-space. The construction is extended to nonsquare games where, in addition to exponentially long Lemke-Howson computations, finding an equilibrium by support enumeration takes on average exponential time. Copyright The Econometric Society 2006.

Suggested Citation

  • Rahul Savani & Bernhard Stengel, 2006. "Hard-to-Solve Bimatrix Games," Econometrica, Econometric Society, vol. 74(2), pages 397-429, March.
    • Handle: RePEc:ecm:emetrp:v:74:y:2006:i:2:p:397-429
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2006.00667.x
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