Trading Favors: Optimal Exchange and Forgiveness

Christine Hauser and Hugo Hopenhayn

No 88, Carlo Alberto Notebooks from Collegio Carlo Alberto

Abstract: How is cooperation without immediate reciprocity sustained in a long term relationship? We study the case of two players in continuous time who have privately observable opportunities to provide favors, and where the arrival of these opportunities is a Poisson process. Favors provided by a player give her an entitlement to future favors from her partner. As opposed to a "chips mechanism" where the rate of exchange of favors is one, we allow for two features: first, for the rate of exchange to depend on current entitlements, and second, for the possibility of depreciation or appreciation of entitlements. We show that these two features allow for considerably higher payoffs. We characterize and solve for the Pareto frontier of Public Perfect Equilibria (PPE) and show that it is self-generating. This guarantees that the equilibrium is renegotiation proof. We also find that optimal PPE have two key characteristics: 1) the relative price of favors decreases with a player's entitlement and 2) the disadvantaged player's utility increases over time during periods of no trade, so in the optimal equilibria there is forgiveness.

Keywords: repeated games; jump process; continuous time (search for similar items in EconPapers)
JEL-codes: C63 C73 D81 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2008
New Economics Papers: this item is included in nep-gth
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Citations: View citations in EconPapers (33)

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