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Trading Favors: Optimal Exchange and Forgiveness

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Author Info
Christine Hauser
Hugo Hopenhayn
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.

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Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 88.

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Length: 30 pages
Date of creation: 2008
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Handle: RePEc:cca:wpaper:88

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Related research
Keywords: repeated games; jump process; continuous time;

Find related papers by JEL classification:
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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