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)


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.


Nash Equilibrium Mixed Strategy Pure Strategy Payoff Matrix Mixed Equilibrium 
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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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