IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v66y2009i2p813-829.html
   My bibliography  Save this article

Equilibrium vengeance

Author

Listed:
  • Friedman, Daniel
  • Singh, Nirvikar

Abstract

The efficiency-enhancing role of the vengeance motive is illustrated in a simple social dilemma game in extensive form. Incorporating behavioral noise and observational noise in random interactions in large groups leads to seven continuous families of (short run) Perfect Bayesian equilibria (PBE) that involve both vengeful and non-vengeful types. A new long run evolutionary equilibrium concept, Evolutionary Perfect Bayesian Equilibrium (EPBE), shrinks the equilibrium set to two points. In one EPBE, only the non-vengeful type survives and there are no mutual gains. In the other EPBE, both types survive and reap mutual gains.

Suggested Citation

  • Friedman, Daniel & Singh, Nirvikar, 2009. "Equilibrium vengeance," Games and Economic Behavior, Elsevier, vol. 66(2), pages 813-829, July.
    • Handle: RePEc:eee:gamebe:v:66:y:2009:i:2:p:813-829
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899-8256(08)00185-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Possajennikov, Alex, 2002. "Cooperative Prisoners and Aggressive Chickens: Evolution of Strategies and Preferences in 2x2 Games," Sonderforschungsbereich 504 Publications 02-04, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    2. Daniel Friedman & Nirvikar Singh, 2004. "Vengefulness Evolves in Small Groups," Palgrave Macmillan Books, in: Steffen Huck (ed.), Advances in Understanding Strategic Behaviour, chapter 3, pages 28-54, Palgrave Macmillan.
    3. Gary Charness & Matthew Rabin, 2002. "Understanding Social Preferences with Simple Tests," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(3), pages 817-869.
    4. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 817-868.
    5. Falk, Armin & Fischbacher, Urs, 2006. "A theory of reciprocity," Games and Economic Behavior, Elsevier, vol. 54(2), pages 293-315, February.
    6. Sethi, Rajiv & Somanathan, E., 2003. "Understanding reciprocity," Journal of Economic Behavior & Organization, Elsevier, vol. 50(1), pages 1-27, January.
    7. Efe A. Ok & Levent KoÚkesen, 2000. "Negatively interdependent preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(3), pages 533-558.
    8. Kockesen, Levent & Ok, Efe A. & Sethi, Rajiv, 2000. "The Strategic Advantage of Negatively Interdependent Preferences," Journal of Economic Theory, Elsevier, vol. 92(2), pages 274-299, June.
    9. David K. Levine, 1998. "Modeling Altruism and Spitefulness in Experiment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 1(3), pages 593-622, July.
    10. Huck, Steffen & Oechssler, Jorg, 1999. "The Indirect Evolutionary Approach to Explaining Fair Allocations," Games and Economic Behavior, Elsevier, vol. 28(1), pages 13-24, July.
    11. Arthur J. Robson, 2002. "Evolution and Human Nature," Journal of Economic Perspectives, American Economic Association, vol. 16(2), pages 89-106, Spring.
    12. Martin Dufwenberg & Alec Smith & Matt Van Essen, 2013. "Hold-Up: With A Vengeance," Economic Inquiry, Western Economic Association International, vol. 51(1), pages 896-908, January.
    13. Friedman, Daniel & Singh, Nirvikar, 2003. "Negative Reciprocity: The Coevolution of Memes and Genes," Santa Cruz Department of Economics, Working Paper Series qt8n49r3t2, Department of Economics, UC Santa Cruz.
    14. Theodore C. Bergstrom, 2002. "Evolution of Social Behavior: Individual and Group Selection," Journal of Economic Perspectives, American Economic Association, vol. 16(2), pages 67-88, Spring.
    15. Jacobsen, Hans Jorgen & Jensen, Mogens & Sloth, Birgitte, 2001. "Evolutionary Learning in Signalling Games," Games and Economic Behavior, Elsevier, vol. 34(1), pages 34-63, January.
    16. Güth, W. & Kliemt, H., 1993. "Competition or Co-Operation," Discussion Paper 1993-39, Tilburg University, Center for Economic Research.
    17. Armen A. Alchian, 1950. "Uncertainty, Evolution, and Economic Theory," Journal of Political Economy, University of Chicago Press, vol. 58(3), pages 211-211.
    18. Richard H. Thaler, 2017. "Behavioral Economics," Journal of Political Economy, University of Chicago Press, vol. 125(6), pages 1799-1805.
    19. repec:adr:anecst:y:2001:i:63-64:p:06 is not listed on IDEAS
    20. Abreu, Dilip & Sethi, Rajiv, 2003. "Evolutionary stability in a reputational model of bargaining," Games and Economic Behavior, Elsevier, vol. 44(2), pages 195-216, August.
    21. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    22. Cox, James C. & Friedman, Daniel & Gjerstad, Steven, 2007. "A tractable model of reciprocity and fairness," Games and Economic Behavior, Elsevier, vol. 59(1), pages 17-45, April.
    23. Heifetz, Aviad & Shannon, Chris & Spiegel, Yossi, 2007. "What to maximize if you must," Journal of Economic Theory, Elsevier, vol. 133(1), pages 31-57, March.
    24. Henrich, Joseph, 2004. "Cultural group selection, coevolutionary processes and large-scale cooperation," Journal of Economic Behavior & Organization, Elsevier, vol. 53(1), pages 3-35, January.
    25. Noldeke, Georg & Samuelson, Larry, 1997. "A Dynamic Model of Equilibrium Selection in Signaling Markets," Journal of Economic Theory, Elsevier, vol. 73(1), pages 118-156, March.
    26. Ely, Jeffrey C. & Yilankaya, Okan, 2001. "Nash Equilibrium and the Evolution of Preferences," Journal of Economic Theory, Elsevier, vol. 97(2), pages 255-272, April.
    27. Dufwenberg, Martin & Kirchsteiger, Georg, 2004. "A theory of sequential reciprocity," Games and Economic Behavior, Elsevier, vol. 47(2), pages 268-298, May.
    28. Gary Charness & Matthew Rabin, 1999. "Social preferences: Some simple tests and a new model," Economics Working Papers 441, Department of Economics and Business, Universitat Pompeu Fabra, revised Jan 2000.
    29. Werner Güth & Hartmut Kliemt, 1994. "Competition Or Co-Operation: On The Evolutionary Economics Of Trust, Exploitation And Moral Attitudes," Metroeconomica, Wiley Blackwell, vol. 45(2), pages 155-187, June.
    30. Ok, Efe A. & Vega-Redondo, Fernando, 2001. "On the Evolution of Individualistic Preferences: An Incomplete Information Scenario," Journal of Economic Theory, Elsevier, vol. 97(2), pages 231-254, April.
    31. Friedman, Daniel & Ostrov, Daniel N., 2008. "Conspicuous consumption dynamics," Games and Economic Behavior, Elsevier, vol. 64(1), pages 121-145, September.
    32. Axel Ockenfels & Gary E. Bolton, 2000. "ERC: A Theory of Equity, Reciprocity, and Competition," American Economic Review, American Economic Association, vol. 90(1), pages 166-193, March.
    33. Theodore W. Schultz, 1962. "Reflections on Investment in Man," NBER Chapters, in: Investment in Human Beings, pages 1-8, National Bureau of Economic Research, Inc.
    34. , & , M., 2006. "Information, evolution and utility," Theoretical Economics, Econometric Society, vol. 1(1), pages 119-142, March.
    35. Ernst Fehr & Simon Gächter, 2002. "Altruistic punishment in humans," Nature, Nature, vol. 415(6868), pages 137-140, January.
    36. Wittman, Donald, 1989. "Why Democracies Produce Efficient Results," Journal of Political Economy, University of Chicago Press, vol. 97(6), pages 1395-1424, December.
    37. Frans Van Winden, 2001. "Emotional Hazard Exemplified by Taxation‐Induced Anger," Kyklos, Wiley Blackwell, vol. 54(2‐3), pages 491-506, May.
    38. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    39. Güth Werner & Kliemt Hartmut & Peleg Bezalel, 2000. "Co-evolution of Preferences and Information in Simple Games of Trust," German Economic Review, De Gruyter, vol. 1(1), pages 83-110, February.
    40. Samuelson, Larry, 2001. "Introduction to the Evolution of Preferences," Journal of Economic Theory, Elsevier, vol. 97(2), pages 225-230, April.
    41. Rubin, Paul H & Paul, Chris W, II, 1979. "An Evolutionary Model of Taste for Risk," Economic Inquiry, Western Economic Association International, vol. 17(4), pages 585-596, October.
    42. Armin Falk & Urs Fischbacher, 2001. "Distributional Consequences and Intentions in a Model of Reciprocity," Annals of Economics and Statistics, GENES, issue 63-64, pages 111-129.
    43. Bohnet, Iris & Frey, Bruno S. & Huck, Steffen, 2001. "More Order with Less Law: On Contract Enforcement, Trust, and Crowding," American Political Science Review, Cambridge University Press, vol. 95(1), pages 131-144, March.
    44. Geanakoplos, John & Pearce, David & Stacchetti, Ennio, 1989. "Psychological games and sequential rationality," Games and Economic Behavior, Elsevier, vol. 1(1), pages 60-79, March.
    45. Samuelson,L. & Swinkels,J.M., 2001. "Information and the evolution of the utility function," Working papers 6, Wisconsin Madison - Social Systems.
    46. Rabin, Matthew, 1993. "Incorporating Fairness into Game Theory and Economics," American Economic Review, American Economic Association, vol. 83(5), pages 1281-1302, December.
    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. Yuval Heller & Eyal Winter, 2020. "Biased-Belief Equilibrium," American Economic Journal: Microeconomics, American Economic Association, vol. 12(2), pages 1-40, May.
    2. Guttman, Joel M., 2013. "On the evolution of conditional cooperation," European Journal of Political Economy, Elsevier, vol. 30(C), pages 15-34.
    3. Daniel Friedman & Nirvikar Singh, 2004. "Vengefulness Evolves in Small Groups," Palgrave Macmillan Books, in: Steffen Huck (ed.), Advances in Understanding Strategic Behaviour, chapter 3, pages 28-54, Palgrave Macmillan.
    4. Jean Rabanal & Daniel Friedman, 2014. "Incomplete Information, Dynamic Stability and the Evolution of Preferences: Two Examples," Dynamic Games and Applications, Springer, vol. 4(4), pages 448-467, December.
    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. Friedman, Daniel & Singh, Nirvikar, 2003. "Negative Reciprocity: The Coevolution of Memes and Genes," Santa Cruz Department of Economics, Working Paper Series qt8n49r3t2, Department of Economics, UC Santa Cruz.
    7. Halpern, Joe & Heller, Yuval & Winter, Eyal, 2022. "The Benefits of Coarse Preferences," MPRA Paper 111670, University Library of Munich, Germany.
    8. Jean Paul Rabanal, 2017. "On the Evolution of Continuous Types Under Replicator and Gradient Dynamics: Two Examples," Dynamic Games and Applications, Springer, vol. 7(1), pages 76-92, March.
    9. Jean Paul Rabanal & Daniel Friedman, 2015. "How Moral Codes Evolve in a Trust Game," Games, MDPI, vol. 6(2), pages 1-11, June.
    10. Arce, Daniel G., 2013. "Principals’ preferences for agents with social preferences," Journal of Economic Behavior & Organization, Elsevier, vol. 90(C), pages 154-163.
    11. Schläpfer, Alain, 2024. "Cross-cultural differences in retaliation: Evidence from the soccer field," Journal of Economic Behavior & Organization, Elsevier, vol. 223(C), pages 216-233.

    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. Daniel Friedman & Nirvikar Singh, 2004. "Vengefulness Evolves in Small Groups," Palgrave Macmillan Books, in: Steffen Huck (ed.), Advances in Understanding Strategic Behaviour, chapter 3, pages 28-54, Palgrave Macmillan.
    2. Sethi, Rajiv & Somanathan, E., 2003. "Understanding reciprocity," Journal of Economic Behavior & Organization, Elsevier, vol. 50(1), pages 1-27, January.
    3. Guttman, Joel M., 2013. "On the evolution of conditional cooperation," European Journal of Political Economy, Elsevier, vol. 30(C), pages 15-34.
    4. Carrasco, Jose A. & Harrison, Rodrigo & Villena, Mauricio G., 2022. "Strategic reciprocity and preference formation," Journal of Economic Behavior & Organization, Elsevier, vol. 203(C), pages 368-381.
    5. Carrasco, José A. & Harrison, Rodrigo & Villena, Mauricio, 2018. "Interdependent preferences and endogenous reciprocity," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 76(C), pages 68-75.
    6. Christian Korth, 2009. "Reciprocity—An Indirect Evolutionary Analysis," Lecture Notes in Economics and Mathematical Systems, in: Fairness in Bargaining and Markets, chapter 0, pages 35-55, Springer.
    7. Jacobs Martin, 2016. "Accounting for Changing Tastes: Approaches to Explaining Unstable Individual Preferences," Review of Economics, De Gruyter, vol. 67(2), pages 121-183, August.
    8. Tóbiás, Áron, 2023. "Rational Altruism," Journal of Economic Behavior & Organization, Elsevier, vol. 207(C), pages 50-80.
    9. Kranz, Sebastian, 2010. "Moral norms in a partly compliant society," Games and Economic Behavior, Elsevier, vol. 68(1), pages 255-274, January.
    10. Reuben, Ernesto & van Winden, Frans, 2008. "Social ties and coordination on negative reciprocity: The role of affect," Journal of Public Economics, Elsevier, vol. 92(1-2), pages 34-53, February.
    11. van Winden, Frans A.A.M. & Stallen, Mirre & Ridderinkhof, Richard, 2008. "On the Nature, Modeling, and Neural Bases of Social Ties," CEPR Discussion Papers 6950, C.E.P.R. Discussion Papers.
    12. Ernesto Reuben & Frans van Winden, 2004. "Reciprocity and Emotions when Reciprocators know each other," Tinbergen Institute Discussion Papers 04-098/1, Tinbergen Institute.
    13. Bierbrauer, Felix & Netzer, Nick, 2016. "Mechanism design and intentions," Journal of Economic Theory, Elsevier, vol. 163(C), pages 557-603.
    14. Xiao, Erte & Bicchieri, Cristina, 2010. "When equality trumps reciprocity," Journal of Economic Psychology, Elsevier, vol. 31(3), pages 456-470, June.
    15. López-Pérez, Raúl, 2009. "The Power of Words: Why Communication fosters Cooperation and Efficiency," Working Papers in Economic Theory 2009/01, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
    16. Kurt A. Ackermann & Ryan O. Murphy, 2019. "Explaining Cooperative Behavior in Public Goods Games: How Preferences and Beliefs Affect Contribution Levels," Games, MDPI, vol. 10(1), pages 1-34, March.
    17. Reuben, Ernesto & Riedl, Arno, 2013. "Enforcement of contribution norms in public good games with heterogeneous populations," Games and Economic Behavior, Elsevier, vol. 77(1), pages 122-137.
    18. Fehr, Ernst & Schmidt, Klaus M., 2005. "The Economics of Fairness, Reciprocity and Altruism – Experimental Evidence and New Theories," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 66, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    19. Kerschbamer, Rudolf, 2015. "The geometry of distributional preferences and a non-parametric identification approach: The Equality Equivalence Test," European Economic Review, Elsevier, vol. 76(C), pages 85-103.
    20. Becker, Johannes & Hopp, Daniel & Süß, Karolin, 2020. "How altruistic is indirect reciprocity? - Evidence from gift-exchange games in the lab," VfS Annual Conference 2020 (Virtual Conference): Gender Economics 224592, Verein für Socialpolitik / German Economic Association.

    More about this item

    Keywords

    Reciprocity Vengeance Evolutionary perfect Bayesian equilibrium Social dilemmas;

    JEL classification:

    • Z13 - Other Special Topics - - Cultural Economics - - - Economic Sociology; Economic Anthropology; Language; Social and Economic Stratification
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    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:eee:gamebe:v:66:y:2009:i:2:p:813-829. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.