Poor convexity and Nash equilibria in games

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.

The Politics of E-Learning

“…The problem is that this assumption has been proven wrong in numerous empirical studies. While the models assume that players act to maximize their outcomes, humans are sometimes irrational, vary in their motivations, or are altruistic, preferring to make choices that conflict with their best interests but are in line with an ideal state (Colin, 2003;Radzik, 2013;Chiu et al, 2014).…”