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Polytope Games

Author

Listed:
  • R. Bhattacharjee

    (Boston University)

  • F. Thuijsman

    (Maastricht University)

  • O. J. Vrieze

    (Maastricht University)

Abstract

Starting from the definition of a bimatrix game, we restrict the pair of strategy sets jointly, not independently. Thus, we have a set $$P \subset S_m \times S_n$$ , which is the set of all feasible strategy pairs. We pose the question of whether a Nash equilibrium exists, in that no player can obtain a higher payoff by deviating. We answer this question affirmatively for a very general case, imposing a minimum of conditions on the restricted sets and the payoff. Next, we concentrate on a special class of restricted games, the polytope bimatrix game, where the restrictions are linear and the payoff functions are bilinear. Further, we show how the polytope bimatrix game is a generalization of the bimatrix game. We give an algorithm for solving such a polytope bimatrix game; finally, we discuss refinements to the equilibrium point concept where we generalize results from the theory of bimatrix games.

Suggested Citation

  • R. Bhattacharjee & F. Thuijsman & O. J. Vrieze, 2000. "Polytope Games," Journal of Optimization Theory and Applications, Springer, vol. 105(3), pages 567-588, June.
    • Handle: RePEc:spr:joptap:v:105:y:2000:i:3:d:10.1023_a:1004689006566
    DOI: 10.1023/A:1004689006566
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    References listed on IDEAS

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    1. Borm, P.E.M. & Jansen, M.J.M. & Potters, J.A.M. & Tijs, S.H., 1993. "On the structure of the set of perfect equilibria in bimatrix games," Other publications TiSEM 5a4170b8-1cb6-416f-b944-e, Tilburg University, School of Economics and Management.
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