This paper considers bimatrix games with matrices having concavity properties. The games described by such payoff matrices well approximate two-person non-zero-sum games on the unit square, with payoff functions F₁(x,y) concave in x for each y, and/or F₂(x,y) concave in y for each x. For these games it is shown that there are Nash equilibria in players' strategies with supports consisting of at most two points. Also a simple search procedure for such Nash equilibria is given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am33-1-6,
author = {Wojciech Po\l owczuk},
title = {On two-point Nash equilibria in bimatrix games with convexity properties},
journal = {Applicationes Mathematicae},
volume = {33},
year = {2006},
pages = {71-84},
zbl = {1152.91306},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am33-1-6}
}
Wojciech Połowczuk. On two-point Nash equilibria in bimatrix games with convexity properties. Applicationes Mathematicae, Tome 33 (2006) pp. 71-84. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am33-1-6/