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Salary Competition in Matching Markets with Private Information

Boosey, Luke A. (2011) Salary Competition in Matching Markets with Private Information. Social Science Working Paper, 1353. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20170727-111603591

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Abstract

We analyze a game in which firms with private information compete for workers by making a single salary offer. Once salaries are chosen, firms make offers to workers, who care only about salary. Firms and workers are matched according to the Gale-Shapley deferred acceptance algorithm that dominates the theory of two-sided matching. For a two-firm, two-worker model, we prove existence of a Bayesian Nash equilibrium in which each firm type chooses a salary according to a continuous distribution with interval support in the salary space. We find a ‘separation’ of types in equilibrium, in the sense that between two types with a common most preferred worker, one type always makes higher offers than the other type. The type that makes the higher offers depends on the relative marginal values attached to the workers by the different firm types. Moreover, more ‘popular’ workers attract higher average equilibrium salaries. We also consider an extension of the model to larger markets by replicating the two- firm two-worker case, in order to examine the effects of market size on competition and equilibrium salaries. In the limit, there is no aggregate uncertainty about the realization of firm types. We characterize the equilibria for this limit case in which there are a continuum of firms and a continuum of workers divided into two equal-sized worker classes. Finally, we conjecture the existence and convergence of the sequence of equilibria in finite replicated markets to the corresponding continuum equilibrium as the number of replications approaches infinity.


Item Type:Report or Paper (Working Paper)
Additional Information:I would like to thank John Ledyard, Federico Echenique, Jean-Laurent Rosenthal, Salvatore Nunnari, Sang-Mok Lee, and Cary Frydman for their many useful comments. I would also like to thank participants at the Canadian Economic Theory Conference and the North American Summer Meetings of the Econometric Society for their comments and suggestions.
Group:Social Science Working Papers
Subject Keywords:Salary competition, Two-sided markets, Bayesian games, Replicated markets
Classification Code:JEL: C72, C78, D82, J41
Record Number:CaltechAUTHORS:20170727-111603591
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170727-111603591
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79491
Collection:CaltechAUTHORS
Deposited By: Hanna Storlie
Deposited On:02 Aug 2017 21:37
Last Modified:02 Aug 2017 21:37

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