Abstract
The two-sided matching literature has focused on static and centralized games. However, in many markets, the matching is determined in decentralized fashion and continues to change. This paper considers infinitely-repeated matching games, where firms whose positions become vacant make offers to workers, who then decide which offers to accept and the game continues. We study how the stationary-equilibrium outcome depends on whether players commit to their employment relationships. We show that, without commitment from either side of the market (i.e., each contract expires in a period), the equilibrium matching is stable in all periods. With one-sided commitment (where firms offer tenured jobs) or two-sided commitment, the final matching may be unstable. With one-sided commitment, the final matching may be one where all workers are worse off and all firms are better off than in every stable matching, implying that the workers are made worse off by job protection.
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