IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v146y2011i5p2013-2028.html
   My bibliography  Save this article

Quantal response equilibria with heterogeneous agents

Author

Listed:
  • Russell, Golman

Abstract

This paper introduces a model of quantal response equilibrium with heterogeneous agents and demonstrates the existence of a representative agent for such populations. Except in rare cases, the representative agentʼs noise terms cannot be independently and identically distributed across the set of actions, even if that is assumed for the individual agents. This result demonstrates a fundamental difference between a representative agent and truly heterogeneous quantal responders and suggests that when fitting quantal response specifications to aggregate data from a population of subjects, the noise terms should be allowed to be jointly dependent across actions. Even though this introduces additional degrees of freedom, it makes the model well specified. The representative agent inherits a regular quantal response function from the actual agents, so this model does impose falsifiable restrictions.

Suggested Citation

  • Russell, Golman, 2011. "Quantal response equilibria with heterogeneous agents," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2013-2028, September.
    • Handle: RePEc:eee:jetheo:v:146:y:2011:i:5:p:2013-2028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053111000913
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    References listed on IDEAS

    as
    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. McKelvey, Richard D. & Palfrey, Thomas R. & Weber, Roberto A., 2000. "The effects of payoff magnitude and heterogeneity on behavior in 2 x 2 games with unique mixed strategy equilibria," Journal of Economic Behavior & Organization, Elsevier, vol. 42(4), pages 523-548, August.
    3. Philip A. Haile & Ali Hortaçsu & Grigory Kosenok, 2008. "On the Empirical Content of Quantal Response Equilibrium," American Economic Review, American Economic Association, vol. 98(1), pages 180-200, March.
    4. Rogers, Brian W. & Palfrey, Thomas R. & Camerer, Colin F., 2009. "Heterogeneous quantal response equilibrium and cognitive hierarchies," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1440-1467, July.
    5. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    6. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    7. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
    8. Teck H. Ho & Xin Wang & Colin F. Camerer, 2008. "Individual Differences in EWA Learning with Partial Payoff Information," Economic Journal, Royal Economic Society, vol. 118(525), pages 37-59, January.
    9. Jacob Goeree & Charles Holt & Thomas Palfrey, 2005. "Regular Quantal Response Equilibrium," Experimental Economics, Springer;Economic Science Association, vol. 8(4), pages 347-367, December.
    10. Tesfatsion, Leigh & Judd, Kenneth L., 2006. "Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics," Staff General Research Papers Archive 10368, Iowa State University, Department of Economics.
    11. Weizsacker, Georg, 2003. "Ignoring the rationality of others: evidence from experimental normal-form games," Games and Economic Behavior, Elsevier, vol. 44(1), pages 145-171, July.
    12. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    13. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
    14. Hofbauer, Josef & Hopkins, Ed, 2005. "Learning in perturbed asymmetric games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 133-152, July.
    15. Hofbauer, Josef & Sandholm, William H., 2007. "Evolution in games with randomly disturbed payoffs," Journal of Economic Theory, Elsevier, vol. 132(1), pages 47-69, January.
    16. Hopkins, Ed, 1999. "A Note on Best Response Dynamics," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 138-150, October.
    17. Leigh Tesfatsion & Kenneth L. Judd (ed.), 2006. "Handbook of Computational Economics," Handbook of Computational Economics, Elsevier, edition 1, volume 2, number 2.
    18. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 2004. "Noisy Directional Learning and the Logit Equilibrium," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(3), pages 581-602, October.
    19. Alan Kirman, 2006. "Heterogeneity in Economics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 1(1), pages 89-117, May.
    20. Nathaniel T Wilcox, 2006. "Theories of Learning in Games and Heterogeneity Bias," Econometrica, Econometric Society, vol. 74(5), pages 1271-1292, September.
    21. TeckH. Ho & Xin Wang & ColinF. Camerer, 2008. "Individual Differences in EWA Learning with Partial Payoff Information," Economic Journal, Royal Economic Society, vol. 118(525), pages 37-59, January.
    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. Yariv, Leeat & Jackson, Matthew O., 2018. "The Non-Existence of Representative Agents," CEPR Discussion Papers 13397, C.E.P.R. Discussion Papers.
    2. Lim, Wooyoung & Matros, Alexander & Turocy, Theodore L., 2014. "Bounded rationality and group size in Tullock contests: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 99(C), pages 155-167.
    3. Benjamin Patrick Evans & Sumitra Ganesh, 2024. "Learning and Calibrating Heterogeneous Bounded Rational Market Behaviour with Multi-Agent Reinforcement Learning," Papers 2402.00787, arXiv.org.
    4. Golman, Russell, 2012. "Homogeneity bias in models of discrete choice with bounded rationality," Journal of Economic Behavior & Organization, Elsevier, vol. 82(1), pages 1-11.

    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. Golman, Russell, 2012. "Homogeneity bias in models of discrete choice with bounded rationality," Journal of Economic Behavior & Organization, Elsevier, vol. 82(1), pages 1-11.
    2. Benaïm, Michel & Hofbauer, Josef & Hopkins, Ed, 2009. "Learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1694-1709, July.
    3. Alan Kirman & François Laisney & Paul Pezanis-Christou, 2023. "Relaxing the symmetry assumption in participation games: a specification test for cluster-heterogeneity," Experimental Economics, Springer;Economic Science Association, vol. 26(4), pages 850-878, September.
    4. Cason, Timothy N. & Friedman, Daniel & Hopkins, Ed, 2010. "Testing the TASP: An experimental investigation of learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2309-2331, November.
    5. Xie, Erhao, 2021. "Empirical properties and identification of adaptive learning models in behavioral game theory," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 798-821.
    6. Chen, Shu-Heng, 2012. "Varieties of agents in agent-based computational economics: A historical and an interdisciplinary perspective," Journal of Economic Dynamics and Control, Elsevier, vol. 36(1), pages 1-25.
    7. Kirman, Alan P. & Laisney, François & Pezanis-Christou, Paul, 2018. "Exploration vs exploitation, impulse balance equilibrium, and a specification test for the El Farol bar problem," ZEW Discussion Papers 18-038, ZEW - Leibniz Centre for European Economic Research.
    8. repec:ehu:ikerla:9171 is not listed on IDEAS
    9. Zhang, Boyu & Hofbauer, Josef, 2016. "Quantal response methods for equilibrium selection in 2×2 coordination games," Games and Economic Behavior, Elsevier, vol. 97(C), pages 19-31.
    10. Fudenberg, Drew & Takahashi, Satoru, 2011. "Heterogeneous beliefs and local information in stochastic fictitious play," Games and Economic Behavior, Elsevier, vol. 71(1), pages 100-120, January.
    11. Hofbauer, Josef & Hopkins, Ed, 2005. "Learning in perturbed asymmetric games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 133-152, July.
    12. Russell Golman, 2011. "Why learning doesn’t add up: equilibrium selection with a composition of learning rules," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 719-733, November.
    13. Benndorf, Volker & Martínez-Martínez, Ismael, 2017. "Perturbed best response dynamics in a hawk–dove game," Economics Letters, Elsevier, vol. 153(C), pages 61-64.
    14. Mertikopoulos, Panayotis & Sandholm, William H., 2018. "Riemannian game dynamics," Journal of Economic Theory, Elsevier, vol. 177(C), pages 315-364.
    15. Ratul, Lahkar, 2011. "The dynamic instability of dispersed price equilibria," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1796-1827, September.
    16. Jakub Bielawski & Thiparat Chotibut & Fryderyk Falniowski & Michal Misiurewicz & Georgios Piliouras, 2022. "Unpredictable dynamics in congestion games: memory loss can prevent chaos," Papers 2201.10992, arXiv.org, revised Jan 2022.
    17. Camerer, Colin F. & Ho, Teck-Hua, 2015. "Behavioral Game Theory Experiments and Modeling," Handbook of Game Theory with Economic Applications,, Elsevier.
    18. Josephson, Jens, 2008. "A numerical analysis of the evolutionary stability of learning rules," Journal of Economic Dynamics and Control, Elsevier, vol. 32(5), pages 1569-1599, May.
    19. Kets, W., 2008. "Networks and learning in game theory," Other publications TiSEM 7713fce1-3131-498c-8c6f-3, Tilburg University, School of Economics and Management.
    20. Lahkar, Ratul & Riedel, Frank, 2015. "The logit dynamic for games with continuous strategy sets," Games and Economic Behavior, Elsevier, vol. 91(C), pages 268-282.
    21. Panayotis Mertikopoulos & William H. Sandholm, 2016. "Learning in Games via Reinforcement and Regularization," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1297-1324, November.

    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:jetheo:v:146:y:2011:i:5:p:2013-2028. 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/622869 .

    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.