Endogenous Mechanisms and Nash Equilibrium in Competitive Contracting
AbstractWe 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.
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Bibliographic InfoPaper provided by Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington in its series Caepr Working Papers with number 2007-025.
Length: 23 pages
Date of creation: Nov 2007
Date of revision:
common agency with adverse selection; endogenous contracting mechanisms; discontinuous games; catalog games; existence of Nash equilibrium; competitive contracting;
Find related papers by JEL classification:
- C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
- C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
- D4 - Microeconomics - - Market Structure and Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-11-17 (All new papers)
- NEP-COM-2007-11-17 (Industrial Competition)
- NEP-GTH-2007-11-17 (Game Theory)
- NEP-MIC-2007-11-17 (Microeconomics)
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