A Matrix Representation of an n-Person 0-1 Game and Its 0-1 Tail Algorithm to Find (Strictly) Pure Nash Equilibria

摘要

An n-person double action game, i.e., an n-person strategy game, i.e., every player has and only has two actions, is a typical and useful game. It has been proved that in an n-person double game, every player's two actions can be denoted by 0 and 1. An n-person double action game, i.e., every player's action set is denoted as {0,1}, is said to be an n-person 0-1 game. In this paper, we first give a matrix representation of an n-person 0-1 game and then give a new and simpler algorithm to find all the (strictly) pure Nash equilibria for an n-person 0-1 game, called 0-1 tail algorithm. Specially, this algorithm can be simplified if the game is symmetrical. Some examples are given to show the algorithm.