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 this paper we extend the basic model of Cournot competition to the case where both the demand function and the cost functions of each firm depend on the amounts produced by competitors. In this modified setting, proving existence of equilibria becomes harder. We develop a generalization of...

The intuitive idea of two activities being complements, for example tea and lemon, is that increasing the level of one makes somehow desirable to increase the level of the other (Samuelson, 1974). Hence complementarity, in its very nature, is a sensitivity property of the set of solutions to an...

We introduce a class of games with complementarities that has the quasisupermodular games, hence the supermodular games, as a special case. Our games retain the main property of quasisupermodular games: the Nash set is a nonempty complete lattice. We use monotonicity properties on the best reply...

We show that the main theorem in Al-Najjar’s 1995 Econometrica paper is false. We provide additional references for the residual implications that are valid, but point out that these stan- dard implications are incapable of bearing the interpretative weight that Al-Najjar places on them.

The standard state-spaces of asymmetric information preclude non-trivial forms of unawareness (Dekel, Lipman and Rustichini, 1998). We introduce a generalized state-space model that allows for non-trivial unawareness among several individuals, and which satisfies strong properties of knowledge...

In perfectly competitive economies under uncertainty, there is a well-known equivalence between a formulation with contingent goods and a formulation with state-specific securities followed by spot markets for goods. In this paper, I examine whether this equivalence carries over in a particular...

The literature on supermodular optimization and games is surveyed from the perspective of potential users in economics. This methodology provides a new approach for comparative statics based only on critical assumptions, and allows a general analysis of games with strategic complementarities....

In the first part of this paper we prove that the global quadratic optimization problem over a simplex can be solved with a constant relative accuracy. In the second part we consider some natural extensions of the result.

We present a convex conic relaxation for a problem of maximising an indefinite quadratic form over a set of convex constraints on the squared variables. We show that for all these problems we get at least 12/37 relative accuracy of the approximation. In the second part of the paper we derive the...