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Trading Favors: Optimal Exchange and Forgiveness

Author

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  • 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.

Suggested Citation

  • Christine Hauser & Hugo Hopenhayn, 2008. "Trading Favors: Optimal Exchange and Forgiveness," Carlo Alberto Notebooks 88, Collegio Carlo Alberto.
    • Handle: RePEc:cca:wpaper:88
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    Citations

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    Cited by:

    1. Guo, Yingni & Hörner, Johannes, 2015. "Dynamic Mechanisms without Money," Economics Series 310, Institute for Advanced Studies.
    2. Atila Abdulkadiroglu & Kyle Bagwell, 2013. "Trust, Reciprocity, and Favors in Cooperative Relationships," American Economic Journal: Microeconomics, American Economic Association, vol. 5(2), pages 213-259, May.
    3. Jean Guillaume Forand & Jan Zapal, 2017. "The Demand and Supply of Favours in Dynamic Relationships," CERGE-EI Working Papers wp605, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    4. Thomas Wiseman, 2015. "A Note on the Essentiality of Money under Limited Memory," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 18(4), pages 881-893, October.
    5. Batista, Catia & Silverman, Dan & Yang, Dean, 2015. "Directed giving: Evidence from an inter-household transfer experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 118(C), pages 2-21.
    6. Sanktjohanser, Anna & Hörner, Johannes, 2022. "Too Much of A Good Thing?," TSE Working Papers 22-1327, Toulouse School of Economics (TSE).
    7. Matthew Mitchell, 2018. "Free (Ad)vice," 2018 Meeting Papers 1194, Society for Economic Dynamics.
    8. George J. Mailath & Andrew Postlewaite & Larry Samuelson, 2016. "Buying Locally," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(4), pages 1179-1200, November.
    9. de Clippel, Geoffroy & Eliaz, Kfir & Fershtman, Daniel & Rozen, Kareen, 2021. "On selecting the right agent," Theoretical Economics, Econometric Society, vol. 16(2), May.
    10. Johannes Hörner & Anna Sanktjohanser, 2022. "Too Much of A Good Thing?," Working Papers hal-03632455, HAL.
    11. Olszewski, Wojciech & Safronov, Mikhail, 2018. "Efficient chip strategies in repeated games," Theoretical Economics, Econometric Society, vol. 13(3), September.
    12. Compte, Olivier & Postlewaite, Andrew, 2015. "Plausible cooperation," Games and Economic Behavior, Elsevier, vol. 91(C), pages 45-59.
    13. Olszewski, Wojciech & Safronov, Mikhail, 2018. "Efficient cooperation by exchanging favors," Theoretical Economics, Econometric Society, vol. 13(3), September.
    14. Lipnowski, Elliot & Ramos, João, 2020. "Repeated delegation," Journal of Economic Theory, Elsevier, vol. 188(C).
    15. Arina Nikandrova & Jevgenijs Steinbuks, 2017. "Contracting for the second best in dysfunctional electricity markets," Journal of Regulatory Economics, Springer, vol. 51(1), pages 41-71, February.
    16. Itai Ashlagi & Alvin E. Roth, 2021. "Kidney Exchange: An Operations Perspective," Management Science, INFORMS, vol. 67(9), pages 5455-5478, September.
    17. Guo, Yingni & Hörner, Johannes, 2020. "Dynamic Allocation without Money," TSE Working Papers 20-1133, Toulouse School of Economics (TSE).
    18. Yingni Guo & Johannes Hörner, 2021. "Dynamic Allocation without Money," Working Papers hal-03187506, HAL.
    19. Josef Schroth, 2013. "Fiscal policy coordination in monetary unions," 2013 Meeting Papers 74, Society for Economic Dynamics.
    20. Li, Jin & Powell, Michael, 2020. "Multilateral interactions improve cooperation under random fluctuations," Games and Economic Behavior, Elsevier, vol. 119(C), pages 358-382.
    21. Forand, Jean Guillaume & Zapal, Jan, 2020. "Production priorities in dynamic relationships," Theoretical Economics, Econometric Society, vol. 15(3), July.

    More about this item

    Keywords

    repeated games; jump process; continuous time;
    All these keywords.

    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; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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