Almost Pure Nash Equilibria in Convex Noncooperative Games

Tadeusz Radzik () and Wojciech Połowczuk ()
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Tadeusz Radzik: Wrocław University of Technology
Wojciech Połowczuk: Wrocław University of Technology

A chapter in Generalized Convexity and Related Topics, 2007, pp 433-447 from Springer

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.

Keywords: Noncooperative games; matrix games; Nash equilibrium; convex payoffs; two-point strategies (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-540-37007-9_26

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DOI: 10.1007/978-3-540-37007-9_26

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