Notes on Boolean Functions and Nash Equilibrium

Abstract

Boolean functions are used to represent individuals' decisions, which are functions of other individuals' decisions. Thus, a set of Boolean functions can be used to represent a n-player strategic form game. To find the equilibria of the game is thus to find the fixed points of the Boolean functions. This paper derives an algorithm to find such fixed points. The algorithm is useful when, in a game, the actions of the players are {0,1} decisions, the players are asymmetric, there are many players, and we know the players' decisions but not their payoffs. An example, together with a Matlab program, demonstrates how to use the algorithm to solve a complex decision problem.

Keywords: Boolean algebra, Boolean functions, Boolean tables, fixed points, Matlab programming

JEL Classification: C63, C71, M11