[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/oup/restud/v85y2018i4p2253-2282..html
   My bibliography  Save this article

Observations on Cooperation

Author

Listed:
  • Yuval Heller
  • Erik Mohlin
Abstract
We study environments in which agents are randomly matched to play a Prisoner’s Dilemma, and each player observes a few of the partner’s past actions against previous opponents. We depart from the existing related literature by allowing a small fraction of the population to be commitment types. The presence of committed agents destabilizes previously proposed mechanisms for sustaining cooperation. We present a novel intuitive combination of strategies that sustains cooperation in various environments. Moreover, we show that under an additional assumption of stationarity, this combination of strategies is essentially the unique mechanism to support full cooperation, and it is robust to various perturbations. Finally, we extend the results to a setup in which agents also observe actions played by past opponents against the current partner, and we characterize which observation structure is optimal for sustaining cooperation.

Suggested Citation

  • Yuval Heller & Erik Mohlin, 2018. "Observations on Cooperation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(4), pages 2253-2282.
    • Handle: RePEc:oup:restud:v:85:y:2018:i:4:p:2253-2282.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/restud/rdx076
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Johannes Hörner & Stefano Lovo, 2009. "Belief-Free Equilibria in Games With Incomplete Information," Econometrica, Econometric Society, vol. 77(2), pages 453-487, March.
    2. Engelmann, Dirk & Fischbacher, Urs, 2009. "Indirect reciprocity and strategic reputation building in an experimental helping game," Games and Economic Behavior, Elsevier, vol. 67(2), pages 399-407, November.
    3. Paul R. Milgrom & Douglass C. North & Barry R. Weingast*, 1990. "The Role Of Institutions In The Revival Of Trade: The Law Merchant, Private Judges, And The Champagne Fairs," Economics and Politics, Wiley Blackwell, vol. 2(1), pages 1-23, March.
    4. Robson, A.J., 1989. "Efficiency In Evolutionary Games: Darwin, Nash And Secret Handshake," Papers 89-22, Michigan - Center for Research on Economic & Social Theory.
    5. Christopher Phelan & Andrzej Skrzypacz, 2006. "Private monitoring with infinite histories," Staff Report 383, Federal Reserve Bank of Minneapolis.
    6. Matthew Embrey & Guillaume R Fréchette & Sevgi Yuksel, 2018. "Cooperation in the Finitely Repeated Prisoner’s Dilemma," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(1), pages 509-551.
    7. Jeffrey Ely & Drew Fudenberg & David K. Levine, 2008. "When is reputation bad?," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 10, pages 177-205, World Scientific Publishing Co. Pte. Ltd..
    8. Cripps, Martin W. & Dekel, Eddie & Pesendorfer, Wolfgang, 2005. "Reputation with equal discounting in repeated games with strictly conflicting interests," Journal of Economic Theory, Elsevier, vol. 121(2), pages 259-272, April.
    9. Rosenthal, R W, 1979. "Sequences of Games with Varying Opponents," Econometrica, Econometric Society, vol. 47(6), pages 1353-1366, November.
    10. Drew Fudenberg & David K. Levine, 2008. "Reputation And Equilibrium Selection In Games With A Patient Player," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 7, pages 123-142, World Scientific Publishing Co. Pte. Ltd..
    11. Heller, Yuval & Mohlin, Erik, 2019. "Coevolution of deception and preferences: Darwin and Nash meet Machiavelli," Games and Economic Behavior, Elsevier, vol. 113(C), pages 223-247.
    12. Parikshit Ghosh & Debraj Ray, 1996. "Cooperation in Community Interaction Without Information Flows," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(3), pages 491-519.
    13. József Sákovics & Jakub Steiner, 2012. "Who Matters in Coordination Problems?," American Economic Review, American Economic Association, vol. 102(7), pages 3439-3461, December.
    14. Cripps, Martin W & Thomas, Jonathan P, 1995. "Reputation and Commitment in Two-Person Repeated Games without Discounting," Econometrica, Econometric Society, vol. 63(6), pages 1401-1419, November.
    15. Hitoshi Matsushima & Tomomi Tanaka & Tomohisa Toyama, 2013. "Behavioral Approach to Repeated Games with Private Monitoring," CIRJE F-Series CIRJE-F-879, CIRJE, Faculty of Economics, University of Tokyo.
    16. Matthias Blonski & Peter Ockenfels & Giancarlo Spagnolo, 2011. "Equilibrium Selection in the Repeated Prisoner's Dilemma: Axiomatic Approach and Experimental Evidence," American Economic Journal: Microeconomics, American Economic Association, vol. 3(3), pages 164-192, August.
    17. Heller, Yuval, 2014. "Stability and trembles in extensive-form games," Games and Economic Behavior, Elsevier, vol. 84(C), pages 132-136.
    18. Ingela Alger & Jörgen W. Weibull, 2013. "Homo Moralis—Preference Evolution Under Incomplete Information and Assortative Matching," Econometrica, Econometric Society, vol. 81(6), pages 2269-2302, November.
    19. Marco Celentani & Drew Fudenberg & David K. Levine & Wolfgang Pesendorfer, 2008. "Maintaining A Reputation Against A Long-Lived Opponent," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 9, pages 163-176, World Scientific Publishing Co. Pte. Ltd..
    20. Berger, Ulrich & Grüne, Ansgar, 2016. "On the stability of cooperation under indirect reciprocity with first-order information," Games and Economic Behavior, Elsevier, vol. 98(C), pages 19-33.
    21. Takako Fujiwara-Greve & Masahiro Okuno-Fujiwara, 2009. "Voluntarily Separable Repeated Prisoner's Dilemma," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 993-1021.
    22. Rubinstein, Ariel & Wolinsky, Asher, 1985. "Equilibrium in a Market with Sequential Bargaining," Econometrica, Econometric Society, vol. 53(5), pages 1133-1150, September.
    23. Duffy, John & Ochs, Jack, 2009. "Cooperative behavior and the frequency of social interaction," Games and Economic Behavior, Elsevier, vol. 66(2), pages 785-812, July.
    24. Jimmy Chan, 2000. "On the Non-Existence of Reputation Effects in Two-Person Infinitely-Repeated Games," Economics Working Paper Archive 441, The Johns Hopkins University,Department of Economics.
    25. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    26. Alp E. Atakan & Mehmet Ekmekci, 2012. "Reputation in Long-Run Relationships," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(2), pages 451-480.
    27. Greif, Avner, 1993. "Contract Enforceability and Economic Institutions in Early Trade: the Maghribi Traders' Coalition," American Economic Review, American Economic Association, vol. 83(3), pages 525-548, June.
    28. Takahashi, Satoru, 2010. "Community enforcement when players observe partners' past play," Journal of Economic Theory, Elsevier, vol. 145(1), pages 42-62, January.
    29. Avinash Dixit, 2003. "On Modes of Economic Governance," Econometrica, Econometric Society, vol. 71(2), pages 449-481, March.
    30. Martin A. Nowak & Karl Sigmund, 1998. "Evolution of indirect reciprocity by image scoring," Nature, Nature, vol. 393(6685), pages 573-577, June.
    31. Florian Herold, 2012. "Carrot or Stick? The Evolution of Reciprocal Preferences in a Haystack Model," American Economic Review, American Economic Association, vol. 102(2), pages 914-940, April.
    32. Kim, Yong-Gwan & Sobel, Joel, 1995. "An Evolutionary Approach to Pre-play Communication," Econometrica, Econometric Society, vol. 63(5), pages 1181-1193, September.
    33. Yves Breitmoser, 2015. "Cooperation, but No Reciprocity: Individual Strategies in the Repeated Prisoner's Dilemma," American Economic Review, American Economic Association, vol. 105(9), pages 2882-2910, September.
    34. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    35. Okuno-Fujiwara Masahiro & Postlewaite Andrew, 1995. "Social Norms and Random Matching Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 79-109, April.
    36. Michihiro Kandori, 1992. "Social Norms and Community Enforcement," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(1), pages 63-80.
    37. Bernstein, Lisa, 1992. "Opting Out of the Legal System: Extralegal Contractual Relations in the Diamond Industry," The Journal of Legal Studies, University of Chicago Press, vol. 21(1), pages 115-157, January.
    38. Herold, Florian & Kuzmics, Christoph, 2009. "Evolutionary stability of discrimination under observability," Games and Economic Behavior, Elsevier, vol. 67(2), pages 542-551, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Song, Zhao & Guo, Hao & Jia, Danyang & Perc, Matjaž & Li, Xuelong & Wang, Zhen, 2021. "Third party interventions mitigate conflicts on interdependent networks," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    2. Artyom Jelnov & Yair Tauman & Chang Zhao, 2021. "Stag Hunt with unknown outside options," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(1), pages 303-335, July.
    3. Gaudeul, Alexia & Keser, Claudia & Müller, Stephan, 2021. "The evolution of morals under indirect reciprocity," Games and Economic Behavior, Elsevier, vol. 126(C), pages 251-277.
    4. Florian Gauer & Christoph Kuzmics, 2020. "Cognitive Empathy In Conflict Situations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(4), pages 1659-1678, November.
    5. Heller, Yuval & Mohlin, Erik, 2019. "Coevolution of deception and preferences: Darwin and Nash meet Machiavelli," Games and Economic Behavior, Elsevier, vol. 113(C), pages 223-247.
    6. Bester, Helmut & Sákovics, József, 2024. "Cooperation, competition, and welfare in a matching market," Games and Economic Behavior, Elsevier, vol. 143(C), pages 357-369.
    7. repec:grz:wpaper:2016-02 is not listed on IDEAS
    8. Harry Pei, 2022. "Reputation Effects under Short Memories," Papers 2207.02744, arXiv.org, revised Jan 2023.
    9. Block, Juan I. & Fudenberg, Drew & Levine, David K., 2019. "Learning dynamics with social comparisons and limited memory," Theoretical Economics, Econometric Society, vol. 14(1), January.
    10. Heller, Yuval & Mohlin, Erik, 2018. "Social learning and the shadow of the past," Journal of Economic Theory, Elsevier, vol. 177(C), pages 426-460.
    11. Tom Potoms & Tom Truyts, 2020. "Unhappy is the land without symbols - Group symbols in infinitely repeated public good games," Working Paper Series 1720, Department of Economics, University of Sussex Business School.
    12. Tóbiás, Áron, 2023. "Rational Altruism," Journal of Economic Behavior & Organization, Elsevier, vol. 207(C), pages 50-80.
    13. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    14. Kamei, Kenju, 2020. "The Perverse Costly Signaling Effect on Cooperation under the Shadow of the Future," MPRA Paper 103678, University Library of Munich, Germany.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Heller, Yuval & Mohlin, Erik, 2015. "Stable Observable Behavior," MPRA Paper 63013, University Library of Munich, Germany.
    2. W. Bentley MacLeod, 2006. "Reputations, Relationships and the Enforcement of Incomplete Contracts," CESifo Working Paper Series 1730, CESifo.
    3. Gaudeul, Alexia & Keser, Claudia & Müller, Stephan, 2021. "The evolution of morals under indirect reciprocity," Games and Economic Behavior, Elsevier, vol. 126(C), pages 251-277.
    4. Joyee Deb, 2008. "Cooperation and Community Responsibility: A Folk Theorem for Repeated Matching Games with Names," Working Papers 08-24, New York University, Leonard N. Stern School of Business, Department of Economics.
    5. Atakan, Alp E. & Ekmekci, Mehmet, 2015. "Reputation in the long-run with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 157(C), pages 553-605.
    6. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    7. Balmaceda, Felipe & Escobar, Juan F., 2017. "Trust in cohesive communities," Journal of Economic Theory, Elsevier, vol. 170(C), pages 289-318.
    8. Heller, Yuval & Tubul, Itay, 2023. "Strategies in the repeated prisoner’s dilemma: A cluster analysis," MPRA Paper 117444, University Library of Munich, Germany.
    9. Atakan, Alp Enver & Ekmekci, Mehmet, 2014. "Reputation in Repeated Moral Hazard Games," MPRA Paper 54427, University Library of Munich, Germany.
    10. Bodoh-Creed, Aaron L., 2019. "Endogenous institutional selection, building trust, and economic growth," Games and Economic Behavior, Elsevier, vol. 114(C), pages 169-176.
    11. Wolitzky, Alexander, 2011. "Indeterminacy of reputation effects in repeated games with contracts," Games and Economic Behavior, Elsevier, vol. 73(2), pages 595-607.
    12. Tom Potoms & Tom Truyts, 2020. "Unhappy is the land without symbols - Group symbols in infinitely repeated public good games," Working Paper Series 1720, Department of Economics, University of Sussex Business School.
    13. Lippert, Steffen & Spagnolo, Giancarlo, 2011. "Networks of relations and Word-of-Mouth Communication," Games and Economic Behavior, Elsevier, vol. 72(1), pages 202-217, May.
    14. Monte, Daniel, 2016. "Reputation with one-sided monitoring: Ignorance as a commitment device," Economics Letters, Elsevier, vol. 144(C), pages 18-21.
    15. Salomon, Antoine & Forges, Françoise, 2015. "Bayesian repeated games and reputation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 70-104.
    16. Filip Vesely & Chun-Lei Yang, 2013. "On Optimal Social Convention in Voluntary Continuation Prisoner's Dilemma Games," CESifo Working Paper Series 4553, CESifo.
    17. Fujiwara-Greve, Takako & Okuno-Fujiwara, Masahiro & Suzuki, Nobue, 2012. "Voluntarily separable repeated Prisonerʼs Dilemma with reference letters," Games and Economic Behavior, Elsevier, vol. 74(2), pages 504-516.
    18. Juan Escobar, 2008. "Cooperation and Self-Governance in Heterogeneous Communities," Discussion Papers 07-038, Stanford Institute for Economic Policy Research.
    19. Mailath, George J. & Samuelson, Larry, 2015. "Reputations in Repeated Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    20. Xie, Huan & Lee, Yong-Ju, 2012. "Social norms and trust among strangers," Games and Economic Behavior, Elsevier, vol. 76(2), pages 548-555.

    More about this item

    Keywords

    Community enforcement; Indirect reciprocity; Random matching; Prisoner’s dilemma; Image scoring;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:oup:restud:v:85:y:2018:i:4:p:2253-2282.. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/restud .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.