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Almost Pure Nash Equilibria in Convex Noncooperative Games

In: Generalized Convexity and Related Topics

Author

Listed:
  • Tadeusz Radzik

    (Wrocław University of Technology)

  • Wojciech Połowczuk

    (Wrocław University of Technology)

Abstract

Summary This paper considers n-person non-coalitional games with finite players’ strategy spaces and payoff functions having some concavity or convexity properties. For such games it is shown that there are two-point Nash equilibria in them, that is equilibria in players’ strategies with support consisting of at most two points. The structure of such simple equilibria is discussed in different cases. The results obtained in the paper can be seen as a discrete counterpart of Glicksberg’s theorem and other known results about the existence of pure (or “almost pure”) Nash equilibria in continuous concave (convex) games with compact convex spaces of players’ pure strategies.

Suggested Citation

  • Tadeusz Radzik & Wojciech Połowczuk, 2007. "Almost Pure Nash Equilibria in Convex Noncooperative Games," Lecture Notes in Economics and Mathematical Systems, in: Generalized Convexity and Related Topics, pages 433-447, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-37007-9_26
    DOI: 10.1007/978-3-540-37007-9_26
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