Generic 4×4 Two Person Games Have at Most 15 Nash Equilibria

Computing Equilibria for Two-person Games

Computing Equilibria for Two-Person Games

This paper is a self-contained survey of algorithms for computing Nash equilibria of two-person games given in normal form or extensive form. The classical Lemke{Howson algorithm for nding one equilibrium of a bimatrix game is presented graph-theoretically as well as algebraically in terms of complementary pivoting. Common deenitions of degenerate games are shown as equivalent. Enumeration of a...

On the number of pure Nash equilibria in random two-person games

We study pure Nash equilibria in random two player games, when best replies may be multi valued. We first show that, when all best reply correpondences are equally likely, the probability of at least one pure Nash equilibrium approaches one, and the expected number of pure Nash equilibria approaches infinity, when the size of the game becomes large. We then study the case where the utilities of...

Discovering Theorems in Game Theory: Two-Person Games with Unique Nash Equilibria

In this paper we provide a logical framework for using computers to discover theorems in (two-person finite) games in strategic form, and apply it to discover classes of games that have unique (pure-strategy) Nash equilibria. We consider all possible classes of games that can be expressed by a conjunction of two binary clauses, and our program re-discovered Kats and Thisse’s class of weakly uni...

Generic 4 4 Two Person Games

versity of Minnesota. We are grateful to Bernhard von Stengel and an anonymous referee for helpful comments. Abstract The maximal generic number of Nash equilibria for two person games in which the two agents each have four pure strategies is shown to be 15. In contrast to Keiding (1995), who arrives at this result by referring to the enumeration of Gr unbaum and Sreedharan (1967), our argument...