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.
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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
Alós-Ferrer, C., Shi, F.: Imitation with asymmetric memory. Econ. Theor. 49, 193–215 (2012). https://doi.org/10.1007/s00199-010-0554-x
Andreoni, J., Petrie, R.: Public goods experiments without confidentiality: a glimpse into fund-raising. J. Public Econ. 88, 1605–1623 (2004)
Apesteguia, J., Huck, S., Oechssler, J.: Imitation: theory and experimental evidence. J. Econ. Theory 136, 217–235 (2007)
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)
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)
Beggs, A.W.: On the convergence of reinforcement learning. J. Econ. Theory 122(1), 1–36 (2005)
Bendor, J., Mookherjee, D., Ray, D.: Aspiration-based reinforcement learning in repeated interaction games: an overview. Int. Game Theory Rev. 3, 159–174 (2001a)
Bendor, J., Mookherjee, D., Ray, D.: Reinforcement learning in repeated interaction games. Adv. Theor. Econ. 1(1), 20011004 (2001b)
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)
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
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
Blanes I Vidal, J., Nossol, M.: Tournaments without prizes: evidence from personnel records. Manag. Sci. 57, 1721–1736 (2011)
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)
Börgers, T., Sarin, R.: Learning through reinforcement and replicator dynamics. J. Econ. Theory 77(1), 1–14 (1997)
Börgers, T., Sarin, R.: Naive reinforcement learning with endogenous aspirations. Int. Econ. Rev. 41(4), 921–950 (2000)
Bush, R.R., Mosteller, F.: Stochastic Models for Learning. John Wiley & Sons Inc. (1955)
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)
Charness, G., Masclet, D., Villeval, M.C.: The dark side of competition for status. Manag. Sci. 60(1), 38–55 (2013)
Croson, R., Fatas, E., Neugebauer, T.: Reciprocity, matching and conditional cooperation in two public goods games. Econ. Lett. 87, 95–101 (2005)
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)
Cross, J.G.: A stochastic learning model of economic behavior. Q. J. Econ. 87(2), 239–266 (1973)
Deci, E.: Intrinsic Motivation. Plenum Press, New York (1975)
Dijk, O., Holmen, M., Kirchlet, M.: Rank matters—The impact of social competition on portfolio choice. Eur. Econ. Rev. 66, 97–100 (2014)
Dixon, H.D.: Keeping up with the Joneses: competition and the evolution of collusion. J. Econ. Behav. Organ. 43, 223–238 (2000)
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
Erev, I., Haruvy, E.: Learning and the economics of small decisions. Handb. Exp. Econ. 2, 638–700 (2013)
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)
Erikson, T., Poulsen, A., Villeval, M.C.: Feedback and incentives: experimental evidence. Labour Econ. 16, 679–688 (2009)
Etzioni, A.: Modern Organizations. Prentice-Hall, Englewood Cliffs (1971)
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)
Fatas, E., Heap, S.P.H., Arjona, D.R.: Preference conformism: an experiment. Eur. Econ. Rev. 105, 71–82 (2018)
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)
Fehr, E., Schmidt, K.: A theory of fairness, competition, and cooperation. Q. J. Econ. 114, 817–868 (1999)
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
Fischbacher, U., Gächter, S.: Social preferences, beliefs, and the dynamics of free riding in public goods experiments. Am. Econ. Rev. 100, 541–556 (2010)
Freidlin, M.I., Wentzell, A.D.: Random Perturbations of Dynamical Systems. Springer-Verlag, Berlin (1984)
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)
Gortner, P.J., van der Weele, J.J.: Peer effects and risk sharing in experimental asset markets. Eur. Econ. Rev. 116, 129–147 (2019)
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
Haruvy, E.: On the importance of relative payoffs in two-sided matching. J. Inst. Theor. Econ. 175(1), 58–85 (2019)
Hedlund, J.: Imitation in Cournot oligopolies with multiple markets. Econ. Theor. 60, 567–587 (2015). https://doi.org/10.1007/s00199-015-0878-7
Hedlund, J., Oyarzun, C.: Imitation in heterogeneous populations. Econ. Theor. 65(4), 937–973 (2018). https://doi.org/10.1007/s00199-017-1044-1
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)
Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47, 263–292 (1979)
Kalai, E., Lehrer, E.: Rational learning leads to Nash equilibrium. Econometrica 61, 1019–1045 (1993)
Karandikar, R., Mookherjee, D., Ray, D., Vega-Redondo, F.: Evolving aspirations and cooperation. J. Econ. Theory 80(2), 292–331 (1998)
Lindner, F., Kirchler, M., Rosenkranz, S., Weitzel, U.: Social motives and risk-taking in investment decisions. J. Econ. Dyn. Control 127, 104116 (2021)
Morales, A.J., Fernandez-de-Cordoba, G.: The Walrasian output beats the market. Int. J. Game Theory 41, 209–212 (2012)
Morales, A.J.: Absolutely expedient imitative behavior. Int. J. Game Theory 31, 475–492 (2002)
Oechssler, J.: Cooperation as the result of learning with aspiration levels. J. Econ. Behav. Organ. 49, 405–409 (2002)
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)
Pemantle, R.: A survey of random processes with reinforcement. Probab. Surv. 4, 1–79 (2007)
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)
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)
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)
Rustichini, A.: Optimal properties of stimulus-response learning models. Games Econ. Behav. 29, 244–273 (1999)
Schlag, K.: Why imitate, and if so, how?: a boundedly rational approach to multi-armed bandits. J. Econ. Theory 78, 130–156 (1998)
Schoenberg, E.J., Haruvy, E.: Relative performance information in asset markets: an experimental approach. J. Econ. Psychol. 33, 1143–1155 (2012)
Thorndike, E.L.: Animal Intelligence. MacMillan, New York (1911)
Tran, A., Zuckhauser, R.: Rank as an inherent incentive: evidence from a field experiment. J. Public Econ. 96, 645–650 (2012)
Vega-Redondo, F.: The evolution of Walrasian behavior. Econometrica 65, 375–384 (1997)
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).
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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
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DOI: https://doi.org/10.1007/s00199-024-01560-1
Keywords
- Experiments
- Cournot competition
- Walrasian convergence
- Reinforcement learning
- Endogenous aspiration level
- Social comparison