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Strategic Characterization of the Index of an Equilibrium

  • Arndt von Schemde
  • Bernhard von Stengel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4997)

Abstract

We prove that an equilibrium of a nondegenerate bimatrix game has index + 1 if and only if it can be made the unique equilibrium of an extended game with additional strategies of one player. The main tool is the “dual construction”. A simplicial polytope, dual to the common best-response polytope of one player, has its facets subdivided into best-response regions, so that equilibria are completely labeled points on the surface of that polytope. That surface has dimension m − 1 for an m×n game, which is much lower than the dimension m + n of the polytopes that are classically used.

Keywords

Nash Equilibrium Mixed Strategy Pure Strategy Payoff Matrix Mixed Equilibrium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Arndt von Schemde
    • 1
  • Bernhard von Stengel
    • 1
  1. 1.Department of MathematicsLondon School of EconomicsLondonUnited Kingdom

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