Equilibria in constrained concave bimatrix games

Volume 40 / 2013

Wojciech Połowczuk, Tadeusz Radzik Applicationes Mathematicae 40 (2013), 167-182 MSC: 91A10, 91A05, 91B52. DOI: 10.4064/am40-2-2

Abstract

We study a generalization of bimatrix games in which not all pairs of players' pure strategies are admissible. It is shown that under some additional convexity assumptions such games have equilibria of a very simple structure, consisting of two probability distributions with at most two-element supports. Next this result is used to get a theorem about the existence of Nash equilibria in bimatrix games with a possibility of payoffs equal to $-\infty $. The first of these results is a discrete counterpart of the Debreu Theorem about the existence of pure noncooperative equilibria in $n$-person constrained infinite games. The second one completes the classical theorem on the existence of Nash equilibria in bimatrix games. A wide discussion of the results is given.

Authors

  • Wojciech PołowczukInstitute of Mathematics and Computer Science
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
  • Tadeusz RadzikInstitute of Mathematics and Computer Science
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail

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