Equilibria in constrained concave bimatrix games

Wojciech Połowczuk¹ ; Tadeusz Radzik¹

¹ Institute of Mathematics and Computer Science Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland

Applicationes Mathematicae, Tome 40 (2013) no. 2, pp. 167-182.

Résumé

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.

Détail

DOI : 10.4064/am40-2-2

Keywords: study generalization bimatrix games which pairs players pure strategies admissible shown under additional convexity assumptions games have equilibria simple structure consisting probability distributions two element supports result get theorem about existence nash equilibria bimatrix games possibility payoffs equal infty first these results discrete counterpart debreu theorem about existence pure noncooperative equilibria n person constrained infinite games second completes classical theorem existence nash equilibria bimatrix games wide discussion results given