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Learning Efficient Nash Equilibria in Distributed Systems

  • H Peyton Young
  • Bary S. R. Pradelski

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.

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File URL: http://www.economics.ox.ac.uk/materials/papers/4260/paper480.pdf
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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 480.

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Date of creation: 01 Feb 2010
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Handle: RePEc:oxf:wpaper:480
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Web page: http://www.economics.ox.ac.uk/
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  1. William H. Sandholm, 2002. "Evolutionary Implementation and Congestion Pricing," Review of Economic Studies, Oxford University Press, vol. 69(3), pages 667-689.
  2. Sergiu Hart & Andreu Mas-Colell, 2004. "Stochastic Uncoupled Dynamics and Nash Equilibrium," Levine's Bibliography 122247000000000466, UCLA Department of Economics.
  3. Young, H. Peyton, 2009. "Learning by trial and error," Games and Economic Behavior, Elsevier, vol. 65(2), pages 626-643, March.
  4. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  5. Itai Arieli & Yakov Babichenko, 2011. "Average Testing and the Efficient Boundary," Discussion Paper Series dp567, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  6. H Peyton Young & Jason R. Marden & Lucy Y. Pao, 2011. "Achieving Pareto Optimality Through Distributed Learning," Economics Series Working Papers 557, University of Oxford, Department of Economics.
  7. Peyton Young, 2002. "Learning Hypothesis Testing and Nash Equilibrium," Economics Working Paper Archive 474, The Johns Hopkins University,Department of Economics.
  8. Lawrence E. Blume, 1994. "How Noise Matters," Game Theory and Information 9407002, EconWPA, revised 27 Jul 1994.
  9. Lawrence Blume, 1993. "The Statistical Mechanics of Best-Response Strategy Revision," Game Theory and Information 9307001, EconWPA, revised 26 Jan 1994.
  10. Yakov Babichenko, 2010. "How Long to Pareto Efficiency?," Discussion Paper Series dp562, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  11. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  12. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
  13. Karandikar, Rajeeva & Mookherjee, Dilip & Ray, Debraj & Vega-Redondo, Fernando, 1998. "Evolving Aspirations and Cooperation," Journal of Economic Theory, Elsevier, vol. 80(2), pages 292-331, June.
  14. Yakov Babichenko, 2010. "Completely Uncoupled Dynamics and Nash Equilibria," Discussion Paper Series dp529, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  15. Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, vol. 93(5), pages 1830-1836, December.
  16. 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..
  17. Foster, Dean P. & Young, H. Peyton, 2006. "Regret testing: learning to play Nash equilibrium without knowing you have an opponent," Theoretical Economics, Econometric Society, vol. 1(3), pages 341-367, September.
  18. Sandholm, William H, 2002. "Evolutionary Implementation and Congestion Pricing," Review of Economic Studies, Wiley Blackwell, vol. 69(3), pages 667-89, July.
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