Distributional Strategies for Games with Incomplete Information

Using the notion of “distributional” strategies, this work proves four main theorems: (i) a mixed-strategy Nash equilibrium existence theorem, (ii) a pure-str strategy equilibrium existenceorem, (iii) apure-strategic (epsilon-equilibrium existence theorem), and (iv) a theorem describing how the set of equilibria of a game varies with the parameters of the game.

Abstract

We study games with incomplete information from a point of view which emphasizes the empirical predictions arising from game-theoretic models. Using the notion of “distributional” strategies, we prove four main theorems: (i) a mixed-strategy Nash equilibrium existence theorem, (ii) a pure-strategy equilibrium existence theorem, (iii) a pure-strategy ϵ-equilibrium existence theorem, and (iv) a theorem describing how the set of equilibria of a game varies with the parameters of the game.