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Learning Efficient Nash Equilibria in Distributed Systems

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  • H Peyton Young
  • Bary S. R. Pradelski

Abstract

An individual's learning rule is completely uncoupled if it does not depend on the actions or payoffs of anyone else. We propose a variant of log linear learning that is completely uncoupled and that selects an efficient pure Nash equilibrium in all generic n-person games that possess at least one pure Nash equilibrium. In games that do not have such an equilibrium, there is a simple formula that expresses the long-run probability of the various disequilibrium states in terms of two factors: i) the sum of payoffs over all agents, and ii) the maximum payoff gain that results from a unilateral deviation by some agent. This welfare/stability trade-off criterion provides a novel framework for analyzing the selection of disequilibrium as well as equilibrium states in n-person games.

Suggested Citation

  • H Peyton Young & Bary S. R. Pradelski, 2010. "Learning Efficient Nash Equilibria in Distributed Systems," Economics Series Working Papers 480, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:480
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    References listed on IDEAS

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    3. Yakov Babichenko, 2010. "How Long to Pareto Efficiency?," Discussion Paper Series dp562, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
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    6. Hart, Sergiu & Mas-Colell, Andreu, 2006. "Stochastic uncoupled dynamics and Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 57(2), pages 286-303, November.
    7. Foster, Dean P. & Young, H. Peyton, 2003. "Learning, hypothesis testing, and Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 73-96, October.
    8. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, pages 29-56.
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    13. Sergiu Hart & Yishay Mansour, 2013. "How Long To Equilibrium? The Communication Complexity Of Uncoupled Equilibrium Procedures," World Scientific Book Chapters,in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 10, pages 215-249 World Scientific Publishing Co. Pte. Ltd..
    14. Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, pages 1830-1836.
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    Citations

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    Cited by:

    1. Nax, Heinrich H. & Pradelski, Bary S. R., 2015. "Evolutionary dynamics and equitable core selection in assignment games," LSE Research Online Documents on Economics 65428, London School of Economics and Political Science, LSE Library.
    2. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 195-208.
    3. Nax, Heinrich H. & Burton-Chellew, Maxwell N. & West, Stuart A. & Young, H. Peyton, 2016. "Learning in a black box," Journal of Economic Behavior & Organization, Elsevier, vol. 127(C), pages 1-15.
    4. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," LSE Research Online Documents on Economics 65422, London School of Economics and Political Science, LSE Library.
    5. Juan I Block & Drew Fudenberg & David K Levine, 2017. "Learning Dynamics Based on Social Comparisons," Levine's Working Paper Archive 786969000000001375, David K. Levine.
    6. repec:eee:jeborg:v:138:y:2017:i:c:p:63-68 is not listed on IDEAS
    7. Nax, Heinrich H., 2015. "Equity dynamics in bargaining without information exchange," LSE Research Online Documents on Economics 65426, London School of Economics and Political Science, LSE Library.
    8. Marden, Jason R. & Shamma, Jeff S., 2015. "Game Theory and Distributed Control****Supported AFOSR/MURI projects #FA9550-09-1-0538 and #FA9530-12-1-0359 and ONR projects #N00014-09-1-0751 and #N0014-12-1-0643," Handbook of Game Theory with Economic Applications, Elsevier.
    9. Heinrich Nax & Bary Pradelski, 2015. "Evolutionary dynamics and equitable core selection in assignment games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 903-932, November.
    10. Nax, Heinrich H. & Burton-Chellew, Maxwell N. & West, Stuart A. & Young, H. Peyton, 2016. "Learning in a black box," LSE Research Online Documents on Economics 68714, London School of Economics and Political Science, LSE Library.
    11. Heinrich Nax, 2015. "Equity dynamics in bargaining without information exchange," Journal of Evolutionary Economics, Springer, pages 1011-1026.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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