A Model of Trust Building with Anonymous Re-Matching

Abstract

This paper studies a repeated lender-borrower game with anonymous re-matching (that is, once an ongoing relationship is terminated players are rematched with new partners and prior histories are unobservable). We propose an equilibrium refinement based on two assumptions: (a) default implies termination of the current relationship; (b) in a given relationship, a better loan-repayment history implies weakly higher continuation values for both parties. This refinement captures the idea of "justifiable punishments" in repeated games. We show that, under these conditions, if the discount factor and the re-matching probability are large enough, then the loan size is strictly increasing over time along the equilibrium path of all non-trivial equilibria. As such, this paper helps explain gradualism in long-term relationships, especially credit relationships.

Keywords: gradualism, trust building, moral hazard, social equilibrium, credit relationships

JEL Classification: C72, C73, D86