Multi-attribute bi-matrix games

Abstract

We introduce multi-attribute bi-matrix games and show that a strategy profile is an equilibrium strategy profile with respect to a preference relation satisfying additivity with respect to the zero vector for an arbitrary finite set of  such games having the same number of attributes if and only if it solves a bi-linear programming problem and the value of the objective function at this solution is zero. An immediate consequence of this result, is that if the outcome matrix for the row player is a convex combination of its outcome matrices in the finite collection and the outcome matrix for the column player is a (possibly different) convex combination of its outcome matrices in the finite collection, then a strategy profile is an equilibrium strategy profile for the game associated with pair of matrices if and only if it satisfies the same two conditions.