Games with Complementarities

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 nonemply complete lattice. We use monotonicity properties on the best reply that are weaker than those in the literature, as well as pretty simple and linked with an intuitive idea of complementarity. The sufficient conditions on the payoffs are weaker than those in quasisupermodular games. We also separate the conditions implying existence of a greatest and a least Nash equilibrium from those, stronger, implying that the Nash set is a complete latticeComplementarity, Quasisupermodularity, Supermodular games, Monotone comparative statics, Nash equilibria

Nash equilibria of games with monotonic best replies

We introduce notions of increasingness for the best reply of a game that capture properly the intuitive idea of complementarity among players’ strategies. We show, by generalizing the fixpoint theorems of Veinott and Zhou, that the Nash sets of our games with increasing best replies are nonempty complete lattices. Hence we extend the class of games with strategic complementarities.Complementarity, supermodular games, fixpoint theorem, Nash equilibria

The complementarity foundations of industrial organization

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

Games with complementarities

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 that are weaker than those in the literature, as well as pretty simple and linked with an intuitive idea of complementarity. The sufficient conditions on the payoffs are weaker than those in quasisupermodular games. We also separate the conditions implying existence of a greatest and a least Nash equilibrium from those, stronger, implying that the Nash set is a complete lattice.complementarity, quasisupermodularity, supermodular games, monotone comparative statics, Nash equilibria

A Characterization of Inefficiency in Stochastic Overlapping Generations Economies

In this paper, we provide a characterization of interim inefficiency in stochastic economies of overlapping generations under possibly sequentially incomplete markets. With respect to the established body of results in the literature, we remove the hypothesis of two-period horizons, by considering longer, though uniformly bounded, horizons for generations. The characterization exploits a suitably Modified Cass Criterion, grounded on the long-rung behavior of compounded safe interest rates and independent of the length of horizons of generations. Thus, the hypothesis of two-period horizons is purely heuristic in establishing a criterion for inefficiency. In addition, for sequentially incomplete markets, we adopt a suitable notion of unambiguous inefficiency, separating the inefficient intertemporal allocation of resources from incomplete risk-sharing. Unambiguous inefficiency reduces to inefficiency when markets are sequentially complete.

A characterization of inefficiency in stochastic overlapping generations economies

In this paper, we provide a characterization of interim inefficiency in stochastic economies ofoverlapping generations under possibly sequentially incomplete markets. With respect to the established body of results in the literature, we remove the hypothesis of two-period horizons,by considering longer, though uniformly bounded, horizons for generations. The characterization exploits a suitably Modified Cass Criterion, grounded on the long-run behavior of compounded safe interest rates and independent of the length of horizons of generations. Thus, the hypothesis of two-period horizons is purely heuristic in establishing a criterion for inefficiency. In addition, for sequentially incomplete markets, we adopt a suitable notion of unambiguous inefficiency, separating the inefficient intertemporal allocation of resources from incomplete risk-sharing. Unambiguous inefficiency reduces to inefficiency when markets are sequentially complete.stochastic overlapping generations economies, inefficiency, competitive prices, cass criterion, social security, incomplete markets

A Note On The Characterization Of Inefficiency In Stochastic Overlapping Generations Economies

In this paper, we provide a characterization of interim ine±ciency in stochastic economies of overlapping generations under possibly sequentially incomplete markets. With respect to the established body of results in the literature, we remove the hypothesis of two-period horizons, by considering longer, though uniformly bounded, horizons for generations. The characteri- zation exploits a suitably Modi¯ed Cass Criterion, grounded on the long-rung behavior of compounded safe interest rates and independent of the length of horizons of generations. Thus, the hypothesis of two-period horizons is purely heuristic in establishing a criterion for ine±ciency. In addition, for sequentially incomplete markets, we adopt a suitable notion of unambiguous ine±ciency, separating the ine±cient intertemporal allocation of resources from incomplete risk-sharing. Unambiguous ine±ciency reduces to ine±ciency when markets are sequentially complete.Stochastic overlapping generations economies; ine±ciency; com-

A characterization of inefficiency in stochastic overlapping generations economies

In this paper, we provide a characterization of interim inefficiency in stochastic economies of overlapping generations. With respect to the established body of results in the literature, we allow for sequentially incomplete markets and we remove the hypothesis of two-period horizons, by considering longer, though uniformly bounded, horizons for generations. The characterization exploits a suitably Modified Cass Criterion, based entirely on observable prices and independent of the length of the horizons of generations. For sequentially incomplete markets, we introduce a notion of unambiguous inefficiency, separating the inefficient intertemporal allocation of resources from incomplete risk-sharing. Unambiguous inefficiency reduces to inefficiency when markets are sequentially complete. Furthermore, our analysis shows that the hypothesis of two-period horizons is purely heuristic in establishing a criterion for inefficiency.Stochastic overlapping generations economies Inefficiency Competitive prices Cass Criterion Social security Incomplete markets