The complementarity foundations of industrial organization

Abstract

In this paper we review the state of the art of Games with Strategic Complementarities (GSC), which are fundamental tools in modern Industrial Organization. The originality of the paper lies in the way the material is presented. Indeed, the mathematical aspects of GSC are complex and scattered in a literature which spans a long time period and a variety of research fields such as economics, applied mathematics and operations research. We organize a large amount of material in a unified and self-contained way, and concentrate on the intuitions and conceptual points that lie in the background of the mathematical modeling, with special emphasis on the modeling of complementarity. On the technical side, we investigate in details the choice and content of the assumptions. The scope of the paper is to allow the applied researcher to understand the theory, so that she may rapidly develop her own ability to deal with concrete problems.strategic complementarity, oligopoly theory, supermodularity, Nash equilibria, lattices