Endogenous Mechanisms and Nash Equilibrium in Competitive Contracting

23 Pages Posted: 7 Nov 2007

See all articles by Frank H. Page

Frank H. Page

Indiana University, Bloomington - Department of Economics; Systemic Risk Centre, LSE

Paulo Klinger Monteiro

Getulio Vargas Foundation (FGV) - EPGE

Date Written: November 7, 2007

Abstract

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.

Keywords: common agency with adverse selection, endogenous contracting mechanisms, discontinuous games, catalog games, existence of Nash equilibrium, competitive contracting

JEL Classification: C6, C7, D4

Suggested Citation

Page, Frank H. and Monteiro, Paulo Klinger, Endogenous Mechanisms and Nash Equilibrium in Competitive Contracting (November 7, 2007). CAEPR Working Paper No. 2007-025. Available at SSRN: https://ssrn.com/abstract=1028297 or http://dx.doi.org/10.2139/ssrn.1028297

Frank H. Page (Contact Author)

Indiana University, Bloomington - Department of Economics ( email )

Wylie Hall
Bloomington, IN 47405-6620
United States

Systemic Risk Centre, LSE ( email )

Houghton St
London, WC2A 2AE
United Kingdom

HOME PAGE: http://www.systemicrisk.ac.uk/

Paulo Klinger Monteiro

Getulio Vargas Foundation (FGV) - EPGE ( email )

sala 1103
Rio de Janeiro RJ, 22250-900
Brazil
+55 21 37995838 (Phone)
+55 21 25538821 (Fax)

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