Skip to main content
Log in

Social aspiration reinforcement learning in Cournot games

  • Research Article
  • Published:
Economic Theory Aims and scope Submit manuscript

Abstract

We offer theoretical and experimental evidence showing that social aspiration learning converges to the Walrasian outcome in Cournot games. Reinforcement learning converges to the competitive outcome because the Walrasian quantity is the only action that never yields profits below the average profits in the market. Using data from laboratory experiments, we show that when provided with information about average market profits, they positively (negatively) reinforce actions that yield payoffs above (below) the average payoffs in the market. When provided with both rivals’ individual performance and average market profits, both heuristics (imitation and social learning) are combined by subjects and prices and profits are driven further into competitive levels, closer to the Walrasian quantity. Subjects’ tendency to adjust their choices following the social learning heuristics survives and they adopt it as frequently as imitation when both predictions collide.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Alos-Ferrer, C., Ania, A.B.: The evolutionary stability of perfectly competitive behavior. Econ. Theor. 26, 497–516 (2005). https://doi.org/10.1007/s00199-004-0474-8

    Article  Google Scholar 

  • Alós-Ferrer, C., Shi, F.: Imitation with asymmetric memory. Econ. Theor. 49, 193–215 (2012). https://doi.org/10.1007/s00199-010-0554-x

    Article  Google Scholar 

  • Andreoni, J., Petrie, R.: Public goods experiments without confidentiality: a glimpse into fund-raising. J. Public Econ. 88, 1605–1623 (2004)

    Article  Google Scholar 

  • Apesteguia, J., Huck, S., Oechssler, J.: Imitation: theory and experimental evidence. J. Econ. Theory 136, 217–235 (2007)

    Article  Google Scholar 

  • Apesteguia, J., Huck, S., Oechssler, J., Weidenholzer, S.: Imitation and the evolution of Walrasian behavior: theoretically fragile but behaviorally robust. J. Econ. Theory 145, 1603–1617 (2010)

    Article  Google Scholar 

  • Azmat, G., Iriberri, N.: The importance of relative performance feedback information: evidence from a natural experiment using high school students. J. Public Econ. 94(7), 435–452 (2010)

    Article  Google Scholar 

  • Beggs, A.W.: On the convergence of reinforcement learning. J. Econ. Theory 122(1), 1–36 (2005)

    Article  Google Scholar 

  • Bendor, J., Mookherjee, D., Ray, D.: Aspiration-based reinforcement learning in repeated interaction games: an overview. Int. Game Theory Rev. 3, 159–174 (2001a)

    Article  Google Scholar 

  • Bendor, J., Mookherjee, D., Ray, D.: Reinforcement learning in repeated interaction games. Adv. Theor. Econ. 1(1), 20011004 (2001b)

    Google Scholar 

  • Bicchieri, C., Fatas, E., Aldama, A., Casas, A., Deshpande, I., Lauro, M., Parilli, C., Spohn, M., Pereira, P., Wen, R.: In science we (should) trust: expectations and compliance across nine countries during the COVID-19 pandemic. PLoS ONE 16(6), e0252892 (2021)

    Article  Google Scholar 

  • Bilancini, E., Boncinelli, L.: Social coordination with locally observable types. Econ. Theor. 65(4), 975–1009 (2018). https://doi.org/10.1007/s00199-017-1047-y

    Article  Google Scholar 

  • Bilancini, E., Boncinelli, L.: The evolution of conventions under condition-dependent mistakes. Econ. Theor. 69(2), 497–521 (2020). https://doi.org/10.1007/s00199-019-01174-y

    Article  Google Scholar 

  • Blanes I Vidal, J., Nossol, M.: Tournaments without prizes: evidence from personnel records. Manag. Sci. 57, 1721–1736 (2011)

    Google Scholar 

  • Blanton, H., Buunk, B.P., Gibbons, F.X., Kuyper, H.: When better-than-others compare upward: choice of comparison and comparative evaluation as independent predictors of academic performance. J. Personal. Soc. Psychol. 76(3), 420–430 (1999)

    Article  Google Scholar 

  • Börgers, T., Sarin, R.: Learning through reinforcement and replicator dynamics. J. Econ. Theory 77(1), 1–14 (1997)

    Article  Google Scholar 

  • Börgers, T., Sarin, R.: Naive reinforcement learning with endogenous aspirations. Int. Econ. Rev. 41(4), 921–950 (2000)

    Article  Google Scholar 

  • Bush, R.R., Mosteller, F.: Stochastic Models for Learning. John Wiley & Sons Inc. (1955)

    Book  Google Scholar 

  • Buunk, B.P., Gibbons, F.X.: Social comparison: the end of a theory and the emergence of a field. Organ. Behav. Hum. Decis. Process.behav. Hum. Decis. Process 102, 3–21 (2007)

    Article  Google Scholar 

  • Charness, G., Masclet, D., Villeval, M.C.: The dark side of competition for status. Manag. Sci. 60(1), 38–55 (2013)

    Google Scholar 

  • Croson, R., Fatas, E., Neugebauer, T.: Reciprocity, matching and conditional cooperation in two public goods games. Econ. Lett. 87, 95–101 (2005)

    Article  Google Scholar 

  • Croson, R., Fatas, E., Neugebauer, T., Morales, A.J.: Excludability: a laboratory study on forced ranking in team production. J. Econ. Behav. Organ. 114, 13–26 (2015)

    Article  Google Scholar 

  • Cross, J.G.: A stochastic learning model of economic behavior. Q. J. Econ. 87(2), 239–266 (1973)

    Article  Google Scholar 

  • Deci, E.: Intrinsic Motivation. Plenum Press, New York (1975)

    Book  Google Scholar 

  • Dijk, O., Holmen, M., Kirchlet, M.: Rank matters—The impact of social competition on portfolio choice. Eur. Econ. Rev. 66, 97–100 (2014)

    Article  Google Scholar 

  • Dixon, H.D.: Keeping up with the Joneses: competition and the evolution of collusion. J. Econ. Behav. Organ. 43, 223–238 (2000)

    Article  Google Scholar 

  • Duersch, P., Kolb, A., Oechssler, J., Schipper, B.C.: Rage against the machines: how subjects play against learning algorithms. Econ. Theor. 43(3), 407–430 (2010). https://doi.org/10.1007/s00199-009-0446-0

    Article  Google Scholar 

  • Erev, I., Haruvy, E.: Learning and the economics of small decisions. Handb. Exp. Econ. 2, 638–700 (2013)

    Google Scholar 

  • Erev, I., Roth, A.E.: Predicting how people play games: reinforcement learning in experimental games with unique, mixed strategy equilibria. Am. Econ. Rev. 88, 848–881 (1998)

    Google Scholar 

  • Erikson, T., Poulsen, A., Villeval, M.C.: Feedback and incentives: experimental evidence. Labour Econ. 16, 679–688 (2009)

    Article  Google Scholar 

  • Etzioni, A.: Modern Organizations. Prentice-Hall, Englewood Cliffs (1971)

    Google Scholar 

  • Fallucchi, F., Fatas, E., Kölle, F., Weisel, O.: Not all group members are created equal: heterogeneous abilities in inter-group contests. Exp. Econ. 24, 669–697 (2021)

    Article  Google Scholar 

  • Fatas, E., Heap, S.P.H., Arjona, D.R.: Preference conformism: an experiment. Eur. Econ. Rev. 105, 71–82 (2018)

    Article  Google Scholar 

  • Fatas, E., Meléndez-Jiménez, M.A., Solaz, H.: Social hierarchies: a laboratory study on punishment patterns across Networks. Econ. Inq. 58(1), 104–119 (2020)

    Article  Google Scholar 

  • Fehr, E., Schmidt, K.: A theory of fairness, competition, and cooperation. Q. J. Econ. 114, 817–868 (1999)

    Article  Google Scholar 

  • Fischbacher, U.: z-Tree: Zurich toolbox for ready-made economic experiments. Exp. Econ. 10(2), 171–178 (2007). https://doi.org/10.1007/s10683-006-9159-4

    Article  Google Scholar 

  • Fischbacher, U., Gächter, S.: Social preferences, beliefs, and the dynamics of free riding in public goods experiments. Am. Econ. Rev. 100, 541–556 (2010)

    Article  Google Scholar 

  • Freidlin, M.I., Wentzell, A.D.: Random Perturbations of Dynamical Systems. Springer-Verlag, Berlin (1984)

    Book  Google Scholar 

  • Friedman, D., Huck, S., Oprea, R., Weidenholzer, S.: From imitation to collusion: long-run learning in a low-information environment. J. Econ. Theory 155, 185–205 (2015)

    Article  Google Scholar 

  • Gortner, P.J., van der Weele, J.J.: Peer effects and risk sharing in experimental asset markets. Eur. Econ. Rev. 116, 129–147 (2019)

    Article  Google Scholar 

  • Hart, S., Mas-Colell, A.: Stochastic uncoupled dynamics and Nash equilibrium. Games Econ. Behav. 57(2), 286–303 (2006). https://doi.org/10.1016/j.geb.2005.09.007

    Article  Google Scholar 

  • Haruvy, E.: On the importance of relative payoffs in two-sided matching. J. Inst. Theor. Econ. 175(1), 58–85 (2019)

    Google Scholar 

  • Hedlund, J.: Imitation in Cournot oligopolies with multiple markets. Econ. Theor. 60, 567–587 (2015). https://doi.org/10.1007/s00199-015-0878-7

    Article  Google Scholar 

  • Hedlund, J., Oyarzun, C.: Imitation in heterogeneous populations. Econ. Theor. 65(4), 937–973 (2018). https://doi.org/10.1007/s00199-017-1044-1

    Article  Google Scholar 

  • Izquierdo, L.R., Izquierdo, S.S., Gotts, N.M., Polhill, J.G.: Transient and asymptotic dynamics of reinforcement learning in games. Games Econ. Behav. 61(2), 259–276 (2007)

    Article  Google Scholar 

  • Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47, 263–292 (1979)

    Article  Google Scholar 

  • Kalai, E., Lehrer, E.: Rational learning leads to Nash equilibrium. Econometrica 61, 1019–1045 (1993)

    Article  Google Scholar 

  • Karandikar, R., Mookherjee, D., Ray, D., Vega-Redondo, F.: Evolving aspirations and cooperation. J. Econ. Theory 80(2), 292–331 (1998)

    Article  Google Scholar 

  • Lindner, F., Kirchler, M., Rosenkranz, S., Weitzel, U.: Social motives and risk-taking in investment decisions. J. Econ. Dyn. Control 127, 104116 (2021)

    Article  Google Scholar 

  • Morales, A.J., Fernandez-de-Cordoba, G.: The Walrasian output beats the market. Int. J. Game Theory 41, 209–212 (2012)

    Article  Google Scholar 

  • Morales, A.J.: Absolutely expedient imitative behavior. Int. J. Game Theory 31, 475–492 (2002)

    Article  Google Scholar 

  • Oechssler, J.: Cooperation as the result of learning with aspiration levels. J. Econ. Behav. Organ. 49, 405–409 (2002)

    Article  Google Scholar 

  • Palomino, F., Vega-Redondo, F.: Convergence of aspirations and (partial) cooperation in the prisoner’s dilemma. Int. J. Game Theory 28(4), 465–488 (1999)

    Article  Google Scholar 

  • Pemantle, R.: A survey of random processes with reinforcement. Probab. Surv. 4, 1–79 (2007)

    Google Scholar 

  • Posch, M., Pichler, A., Sigmund, K.: The efficiency of adapting aspiration levels. Proc. r. Soc. Lond. Ser. B Biol. Sci. 266(1427), 1427–1435 (1999)

    Article  Google Scholar 

  • Restrepo-Plaza, L., Fatas, E.: When ingroup favoritism is not the social norm a lab-in-the-field experiment with victims and non-victims of conflict in Colombia. J. Econ. Behav. Organ. 194, 363–383 (2022)

    Article  Google Scholar 

  • Roth, A.E., Erev, I.: Learning in extensive-form games: experimental data and simple dynamic models in the intermediate term. Games Econ. Behav. 8(1), 164–212 (1995)

    Article  Google Scholar 

  • Rustichini, A.: Optimal properties of stimulus-response learning models. Games Econ. Behav. 29, 244–273 (1999)

    Article  Google Scholar 

  • Schlag, K.: Why imitate, and if so, how?: a boundedly rational approach to multi-armed bandits. J. Econ. Theory 78, 130–156 (1998)

    Article  Google Scholar 

  • Schoenberg, E.J., Haruvy, E.: Relative performance information in asset markets: an experimental approach. J. Econ. Psychol. 33, 1143–1155 (2012)

    Article  Google Scholar 

  • Thorndike, E.L.: Animal Intelligence. MacMillan, New York (1911)

    Google Scholar 

  • Tran, A., Zuckhauser, R.: Rank as an inherent incentive: evidence from a field experiment. J. Public Econ. 96, 645–650 (2012)

    Article  Google Scholar 

  • Vega-Redondo, F.: The evolution of Walrasian behavior. Econometrica 65, 375–384 (1997)

    Article  Google Scholar 

Download references

Acknowledgements

Antonio acknowledges financial support from research project PY20-00069. Ainhoa acknowledges financial support from Spanish Ministry of Science and Innovation (PID2021- 123053OB-I00), Generalitat Valenciana (AICO/2021/005), and Jaume I University (UJI- B2021-23).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Enrique Fatas.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fatas, E., Morales, A.J. & Jaramillo-Gutiérrez, A. Social aspiration reinforcement learning in Cournot games. Econ Theory (2024). https://doi.org/10.1007/s00199-024-01560-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00199-024-01560-1

Keywords

JEL Classification

Navigation