Geodesic
On two-point Nash equilibria in bimatrix games with convexity properties
Wojciech Po/lowczuk1
1 Institute of Mathematics Wroc/law University of Technology Wybrze/ze Wyspia/nskiego 27 50-370 Wroc/law, Poland
Applicationes Mathematicae, Tome 33 (2006) no. 1, pp. 71-84 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am33-1-6
Keywords: paper considers bimatrix games matrices having concavity properties games described payoff matrices approximate two person non zero sum games unit square payoff functions concave each concave each these games shown there nash equilibria players strategies supports consisting points simple search procedure nash equilibria given

Wojciech Po/lowczuk 1

1 Institute of Mathematics Wroc/law University of Technology Wybrze/ze Wyspia/nskiego 27 50-370 Wroc/law, Poland 
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Wojciech Po/lowczuk. On two-point Nash equilibria in
 bimatrix games with convexity properties. Applicationes Mathematicae, Tome 33 (2006) no. 1, pp. 71-84. doi: 10.4064/am33-1-6

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