On two-point Nash equilibria in bimatrix games with convexity properties
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 $F_1(x,y)$ concave in $x$ for each $y$, and/or $F_2(x,y)$ 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.