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Convergence of aspirations and (partial) cooperation in the prisoner's dilemma


  • Fernando Vega-Redondo

    () (Facultad de Economicas and Instituto Valenciano de Investigaciones Economicas, Universidad de Alicante, E-03071 Alicante, Spain)

  • Frédéric Palomino

    () (CentER, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands)


This paper proposes an aspiration-based dynamic model for cooperation where a large population of agents are matched afresh every period to play a Prisoner's Dilemma. At each point in time, agents hold a common aspiration level which is updated on the basis of some "population statistic", i.e. a certain scalar summary (e.g. average payoff) associated to the current state. On the other hand, those agents who feel "dissatisfied" (relative to current aspiration) switch actions at a rate which is increasing in the magnitude of the dissatisfaction. The resulting process is shown to converge in the long run under quite general conditions. Moreover, if agents are responsive enough, the long-run social state displays some extent of cooperation, with a constant positive fraction of the population (always less than half) choosing to cooperate in every period.

Suggested Citation

  • Fernando Vega-Redondo & Frédéric Palomino, 1999. "Convergence of aspirations and (partial) cooperation in the prisoner's dilemma," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 465-488.
  • Handle: RePEc:spr:jogath:v:28:y:1999:i:4:p:465-488 Note: Received: January 1998/Revised version: October 1998

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    References listed on IDEAS

    1. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-888, July.
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    Cited by:

    1. Dixon, Huw D. & Sbriglia, Patrizia & Somma, Ernesto, 2006. "Learning to collude: An experiment in convergence and equilibrium selection in oligopoly," Research in Economics, Elsevier, vol. 60(3), pages 155-167, September.
    2. Dixon, Huw David, 2000. "Keeping up with the Joneses: competition and the evolution of collusion," Journal of Economic Behavior & Organization, Elsevier, vol. 43(2), pages 223-238, October.
    3. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Gotts, Nicholas M. & Polhill, J. Gary, 2007. "Transient and asymptotic dynamics of reinforcement learning in games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 259-276, November.
    4. Altavilla, Carlo & Luini, Luigi & Sbriglia, Patrizia, 2006. "Social learning in market games," Journal of Economic Behavior & Organization, Elsevier, vol. 61(4), pages 632-652, December.
    5. Enrique Fatás & Francisca Jiménez & Antonio Morales, 2011. "Controlling for initial endowment and experience in binary choice tasks," Journal of Risk and Uncertainty, Springer, vol. 43(3), pages 227-243, December.
    6. Marcin Dziubinski & Jaideep Roy, 2007. "Endogenous Selection of Aspiring and Rational rules in Coordination Games," CEDI Discussion Paper Series 07-14, Centre for Economic Development and Institutions(CEDI), Brunel University.
    7. Robert S. Gazzale, 2009. "Learning to Play Nash from the Best," Department of Economics Working Papers 2009-03, Department of Economics, Williams College.
    8. Huw D. Dixon & Paolo Lupi, "undated". "Learning with a Known Average: A Simulation Study of Alternative Learning Rules," Discussion Papers 97/18, Department of Economics, University of York.
    9. Cui Zhiwei & Zhai Jian & Liu Xuan, 2009. "The Efficiency of Observability and Mutual Linkage," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-36, July.
    10. Alexander Tieman & Harold Houba & Gerard Laan, 2000. "On the level of cooperative behavior in a local-interaction model," Journal of Economics, Springer, vol. 71(1), pages 1-30, February.
    11. Dziubiński, Marcin & Roy, Jaideep, 2012. "Popularity of reinforcement-based and belief-based learning models: An evolutionary approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(3), pages 433-454.
    12. Segismundo S. Izquierdo & Luis R. Izquierdo & Nicholas M. Gotts, 2008. "Reinforcement Learning Dynamics in Social Dilemmas," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 11(2), pages 1-1.
    13. Alexander F. Tieman & Harold Houba & Gerard van der Laan, 1998. "Cooperation in a Multi-Dimensional Local Interaction Model," Game Theory and Information 9803002, EconWPA.
    14. Angelo Antoci & Pier Sacco & Luca Zarri, 2004. "Coexistence of Strategies and Culturally-Specific Common Knowledge: An Evolutionary Analysis," Journal of Bioeconomics, Springer, vol. 6(2), pages 165-194, May.
    15. Bernard GROFMAN & Joseph GODFREY, 2014. "Aspiration Models of Committee Decision Making," Economics Working Paper from Condorcet Center for political Economy at CREM-CNRS 2014-04-ccr, Condorcet Center for political Economy.

    More about this item


    Aspirations · cooperation · bounded rationality;

    JEL classification:

    • D64 - Microeconomics - - Welfare Economics - - - Altruism; Philanthropy; Intergenerational Transfers
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness


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