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Learning, Matching and Aggregation

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  • Ed Hopkins

    (Department of Economics, University of Edinburgh, UK)

Abstract

Fictitious play and ``gradient'' learning are examined in the context of a large population where agents are repeatedly randomly matched. We show that the aggregation of this learning behaviour can be qualitatively different from learning at the level of the individual. This aggregate dynamic belongs to the same class of simply defined dynamic as do several formulations of evolutionary dynamics. We obtain sufficient conditions for convergence and divergence which are valid for the whole class of dynamics. These results are therefore robust to most specifications of adaptive behaviour.

Suggested Citation

  • Ed Hopkins, 1995. "Learning, Matching and Aggregation," Game Theory and Information 9512001, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpga:9512001
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    Cited by:

    1. Hopkins, Ed, 1999. "A Note on Best Response Dynamics," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 138-150, October.
    2. 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.
    3. 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.
    4. Ed Hopkins & Robert M. Seymour, 2002. "The Stability of Price Dispersion under Seller and Consumer Learning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(4), pages 1157-1190, November.
    5. Ted To, 1999. "Risk and evolution," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(2), pages 329-343.
    6. Oyama, Daisuke, 2009. "Agglomeration under forward-looking expectations: Potentials and global stability," Regional Science and Urban Economics, Elsevier, vol. 39(6), pages 696-713, November.
    7. 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.
    8. Takatoshi Tabuchi & Dao‐Zhi Zeng, 2004. "Stability of Spatial Equilibrium," Journal of Regional Science, Wiley Blackwell, vol. 44(4), pages 641-660, November.
    9. Fernando Lozano & Jaime Lozano & Mario García, 2007. "An artificial economy based on reinforcement learning and agent based modeling," Documentos de Trabajo 3907, Universidad del Rosario.
    10. Yannick Viossat, 2015. "Evolutionary dynamics and dominated strategies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 91-113, April.
    11. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    12. Drew Fudenberg & David K Levine, 2006. "An Economists Perspective on Multi-Agent Learning," Levine's Working Paper Archive 784828000000000683, David K. Levine.
    13. Ed Hopkins, "undated". "Price Dispersion: An Evolutionary Approach," Discussion Papers 1996-3, Edinburgh School of Economics, University of Edinburgh.
    14. Ed Hopkins, 2002. "Adaptive Learning Models of Consumer Behaviour (first version)," Edinburgh School of Economics Discussion Paper Series 80, Edinburgh School of Economics, University of Edinburgh.
    15. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    16. Lahkar, Ratul & Seymour, Robert M., 2013. "Reinforcement learning in population games," Games and Economic Behavior, Elsevier, vol. 80(C), pages 10-38.
    17. 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.
    18. Ramsza, Michal & Seymour, Robert M., 2010. "Fictitious play in an evolutionary environment," Games and Economic Behavior, Elsevier, vol. 68(1), pages 303-324, January.

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    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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