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 -∞. 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am40-2-2,
author = {Wojciech Po\l owczuk and Tadeusz Radzik},
title = {Equilibria in constrained concave bimatrix games},
journal = {Applicationes Mathematicae},
volume = {40},
year = {2013},
pages = {167-182},
zbl = {1272.91019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am40-2-2}
}
Wojciech Połowczuk; Tadeusz Radzik. Equilibria in constrained concave bimatrix games. Applicationes Mathematicae, Tome 40 (2013) pp. 167-182. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am40-2-2/