On two-point Nash equilibria in bimatrix games with convexity properties

Volume 33 / 2006

Wojciech Po/lowczuk Applicationes Mathematicae 33 (2006), 71-84 MSC: Primary 91A05. DOI: 10.4064/am33-1-6


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.


  • Wojciech Po/lowczukInstitute of Mathematics
    Wroc/law University of Technology
    Wybrze/ze Wyspia/nskiego 27
    50-370 Wroc/law, Poland

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