Int J Game Theory (2009) 38:453–467 DOI 10.1007/s00182-009-0163-8 ORIGINAL PAPER Nash implementation of competitive equilibria in the job-matching market Takashi Hayashi · Toyotaka Sakai Accepted: 13 May 2009 / Published online: 30 June 2009 © Springer-Verlag 2009 Abstract This paper studies Nash implementation in the job-matching market where each worker works for only one firm and a firm hires as many workers as it wishes. We show that the competitive equilibrium correspondence (CEC) is the smallest Nash implementable correspondence satisfying individual rationality and Pareto indiffer- ence. Furthermore, the CEC is the minimal monotonic extension of the worker-optimal and firm-optimal subcorrespondences. We offer two “good” mechanisms that imple- ment this correspondence in Nash equilibrium. Keywords Job-matching · Many-to-one matching · Nash implementation · Mechanism design · Monotonic extension · Indivisible goods JEL Classification C78 · D78 · J41 1 Introduction We study the job-matching market introduced by Kelso and Crawford (1982) where each worker works for only one firm and a firm hires as many workers as it wishes. We are grateful to two anonymous referees, Tridib Sharma, and especially William Thomson for their very helpful comments. We also thank participants at the UT-ITAM conference. T. Hayashi Department of Economics, University of Texas at Austin, Austin, TX 78712, USA e-mail: th925@eco.utexas.edu URL: http://www.eco.utexas.edu/~th925 T. Sakai (B ) Department of Economics, Yokohama National University, Yokohama 240-8501, Japan e-mail: toyotaka@ynu.ac.jp URL: http://www.geocities.jp/toyotaka_sakai/ 123