Endogenous mechanisms and Nash equilibrium in competitivecontracting games

摘要

We model strategic competition in a market with asymmetric information as a noncoop-erative game in which each firm competes for the business of a buyer of unknown typeby offering the buyer a catalog of products and prices. The timing in our model is Stack-elberg: in the first stage, given the distribution of buyer types known to all firms and thededucible, type-dependent best responses of the agent, firms simultaneously and nonco-operatively 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 induc-tion, this Stackelberg game with asymmetric information reduces to a game over catalogswith payoff indeterminacies. In particular, due to ties within catalogs and/or across cata-logs, corresponding to any catalog profile offered by firms there may be multiple possibleexpected firm payoffs, all consistent with the rational optimizing behavior of the agentfor each of his types. The resolution of these indeterminacies depends on The tie-breakingmechanism which emerges in the market. Because each tie-breaking mechanism induces aparticular game over catalogs, a reasonable candidate would be a tie-breaking mechanismwhich supports a Nash equilibrium in the corresponding catalog game. We call such a mech-anism an endogenous Nash mechanism. The fundamental question we address in this paperis, does there exist an endogenous Nash mechanism—and therefore, does there exist a Nashequilibrium for the catalog game? We show under fairly mild conditions on primitives thatcatalog games naturally possess tie-breaking mechanisms which support Nash equilibria.