Maximal number of mixed Nash equilibria in generic games where each player has two pure strategies

TL;DR

This paper establishes a lower bound on the maximum number of mixed Nash equilibria in generic m-player games where each player has two strategies, showing it is close to the known upper bound.

Contribution

It provides a new lower bound for the maximum number of mixed Nash equilibria in two-strategy m-player games, advancing understanding of equilibrium complexity.

Findings

Lower bound close to the known upper bound

Maximum number of equilibria depends on number of players

Results apply to generic finite games

Abstract

The number of Nash equilibria of the mixed extension of a generic finite game in normal form is finite and odd. This raises the question how large the number can be, depending on the number of players and the numbers of their pure strategies. Here we present a lower bound for the maximal possible number in the case of m-player games where each player has two pure strategies. It is surprisingly close to a known upper bound.