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Learning, Matching and Aggregation

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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.

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  • Ed Hopkins, 1995. "Learning, Matching and Aggregation," ESE Discussion Papers 2, Edinburgh School of Economics, University of Edinburgh.
  • Handle: RePEc:edn:esedps:2
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    1. Romeo, Charles & Sopher, Barry, 1999. "Learning and Decision Costs in One-Person Games," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(4), pages 335-357, July-Aug..
    2. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
    3. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
    4. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
    5. Fudenberg, Drew & Levine, David K, 1993. "Steady State Learning and Nash Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 547-573, May.
    6. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July.
    7. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    8. Samuelson Larry, 1994. "Stochastic Stability in Games with Alternative Best Replies," Journal of Economic Theory, Elsevier, vol. 64(1), pages 35-65, October.
    9. Sugden, Robert, 1989. "Spontaneous Order," Journal of Economic Perspectives, American Economic Association, vol. 3(4), pages 85-97, Fall.
    10. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    11. Ken Binmore & Larry Samuelson, 1994. "Muddling Through: Noisy Equilibrium Selection," Game Theory and Information 9410002, EconWPA.
    12. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-666, May.
    13. Canning, David, 1992. "Average behavior in learning models," Journal of Economic Theory, Elsevier, vol. 57(2), pages 442-472, August.
    14. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    15. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    16. Brown, James N & Rosenthal, Robert W, 1990. "Testing the Minimax Hypothesis: A Re-examination of O'Neill's Game Experiment," Econometrica, Econometric Society, vol. 58(5), pages 1065-1081, September.
    17. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
    18. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
    19. Ken Binmore & Larry Samuelson, 1994. "Muddling Through: Noisy Equilibrium Selection," Game Theory and Information 9410002, EconWPA.
    20. Crawford, Vincent P., 1985. "Learning behavior and mixed-strategy Nash equilibria," Journal of Economic Behavior & Organization, Elsevier, vol. 6(1), pages 69-78, March.
    21. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    22. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
    23. Friedman, Daniel, 1996. "Equilibrium in Evolutionary Games: Some Experimental Results," Economic Journal, Royal Economic Society, vol. 106(434), pages 1-25, January.
    24. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 59-89.
    25. Boylan, Richard T., 1992. "Laws of large numbers for dynamical systems with randomly matched individuals," Journal of Economic Theory, Elsevier, vol. 57(2), pages 473-504, August.
    26. Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, vol. 68(1), pages 258-265, January.
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    1. repec:spr:etbull:v:3:y:2015:i:1:d:10.1007_s40505-014-0062-4 is not listed on IDEAS
    2. Ed Hopkins, "undated". "Price Dispersion: An Evolutionary Approach," Discussion Papers 1996-3, Edinburgh School of Economics, University of Edinburgh.
    3. 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.
    4. Hopkins, Ed, 1999. "A Note on Best Response Dynamics," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 138-150, October.
    5. 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.
    6. Drew Fudenberg & David K Levine, 2006. "An Economists Perspective on Multi-Agent Learning," Levine's Working Paper Archive 784828000000000683, David K. Levine.
    7. 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.
    8. 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.
    9. Ted To, 1999. "Risk and evolution," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(2), pages 329-343.
    10. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.
    11. Ed Hopkins, 2002. "Adaptive Learning Models of Consumer Behaviour (first version)," ESE Discussion Papers 80, Edinburgh School of Economics, University of Edinburgh.
    12. Lahkar, Ratul & Seymour, Robert M., 2013. "Reinforcement learning in population games," Games and Economic Behavior, Elsevier, vol. 80(C), pages 10-38.
    13. 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.
    14. Ramsza, Michal & Seymour, Robert M., 2010. "Fictitious play in an evolutionary environment," Games and Economic Behavior, Elsevier, vol. 68(1), pages 303-324, January.
    15. Takatoshi Tabuchi & Dao-Zhi Zeng, 2004. "Stability of Spatial Equilibrium," Journal of Regional Science, Wiley Blackwell, vol. 44(4), pages 641-660.
    16. Fernando Lozano & Jaime Lozano & Mario García, 2007. "An artificial economy based on reinforcement learning and agent based modeling," DOCUMENTOS DE TRABAJO 003907, UNIVERSIDAD DEL ROSARIO.
    17. 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.

    More about this item

    Keywords

    games; fictitious play; reinforcement learning; evolution;

    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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