Endogenous Mechanisms and Nash Equilibrium in Competitive Contracting
نویسندگان
چکیده
We model strategic competition in a market with asymmetric information as a noncooperative game in which each firm competes for the business of a buyer of unknown type by offering the buyer a catalog of products and prices. The timing in our model is Stackelberg: in the first stage, given the distribution of buyer types known to all firms and the deducible, type-dependent best responses of the agent, firms simultaneously and noncooperatively choose their catalog offers. In the second stage the buyer, knowing his type, chooses a single firm and product-price pair from that firm’s catalog. By backward induction, this Stackelberg game with asymmetric information reduces to a game over catalogs with payoff indeterminacies. In particular, due to ties within catalogs and/or across catalogs, corresponding to any catalog profile offered by firms there may be multiple possible expected firm payoffs, all consistent with the rational optimizing behavior of the agent for each of his types. The resolution of these indeterminacies depends on the tie-breaking mechanism which emerges in the market. Because each tie-breaking mechanism induces a particular game over catalogs, a reasonable candidate would be a tie-breaking mechanism which supports a Nash equilibrium in the corresponding catalog game. We call such a mechanism an endogenous Nash mechanism. The fundamental question we address in this paper is, does there exist an endogenous Nash mechanism and therefore, does there exist a Nash equilibrium for the catalog game? We show under fairly mild conditions on primitives that catalog games naturally possess tie-breaking mechanisms which support Nash equilibria. ∗Visiting Professor, Centre d’Economie de la Sorbonne, Universite Paris 1, Pantheon-Sorbonne. †The first author acknowledges the financial support of Capes/Cofecub project 468/04. This paper was begun while the second author was Visiting Professor, Centre d’Economie de la Sorbonne, Universite Paris 1, Pantheon-Sorbonne in June of 2005. The second author thanks CES and Paris 1 for their support and hospitality. The second author also thanks the Economics Department at Indiana University for financial support. Dendo22.tex
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