The integer linear complementarity problem

Abstract

In this paper we consider the case of the linear complementarity problem where all or some of the variables are required to take integer values. We discuss several applications to economic equilibrium problems and polymatrix games. When the integer variables are bounded, then the problem can be solved using an equivalent linear integer formulation. For the general problem (unbounded case) the problem can be solved using enumeration of the feasible points of a set of mixed zero-one linear inequalities.

Keywords:

• Linear complementarity
• integer programming
• economic equilibrium problems
• polymatrix games