Poor convexity and Nash equilibria in games

Tadeusz Radzik ()

International Journal of Game Theory, 2014, vol. 43, issue 1, 169-192

Abstract: This paper considers two-person non-zero-sum games on the unit square with payoff functions having a new property called poor convexity. This property describes “something between” the classical convexity and quasi-convexity. It is proved that various types of such games have Nash equilibria with a very simple structure, consisting of the players’ mixed strategies with at most two-element supports. Since poor convexity is a basic notion in the paper, also a theory of poorly convex functions is also developed. Copyright The Author(s) 2014

Keywords: Nash equilibrium; Two-person sum game; Non-zero sum game; Two-point strategy; Poor convexity (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s00182-013-0379-5

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