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How long to Pareto efficiency?

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  • Yakov Babichenko

Abstract

We consider uncoupled dynamics (each player knows only his own payoff function) that reach outcomes that are Pareto efficient and individually rational. We show that in the worst case the number of periods it takes to reach these outcomes must be exponential in the number of players and hence the same number of periods it takes to reach Nash equilibria. For social welfare maximizing outcomes we provide a tight bound on the minimal number of steps required for reaching such an outcome by uncoupled dynamics. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Yakov Babichenko, 2014. "How long to Pareto efficiency?," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 13-24, February.
    • Handle: RePEc:spr:jogath:v:43:y:2014:i:1:p:13-24
    DOI: 10.1007/s00182-013-0365-y
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    References listed on IDEAS

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    1. Sergiu Hart & Andreu Mas-Colell, 2013. "Stochastic Uncoupled Dynamics And Nash Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 8, pages 165-189, World Scientific Publishing Co. Pte. Ltd..
    2. H Peyton Young & Jason R. Marden and Lucy Y. Pao, 2011. "Achieving Pareto Optimality Through Distributed Learning," Economics Series Working Papers 557, University of Oxford, Department of Economics.
    3. 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..
    4. 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.
    5. Sergiu Hart & Andreu Mas-Colell, 2013. "Uncoupled Dynamics Do Not Lead To Nash Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 7, pages 153-163, World Scientific Publishing Co. Pte. Ltd..
    6. Saari, Donald G & Simon, Carl P, 1978. "Effective Price Mechanisms," Econometrica, Econometric Society, vol. 46(5), pages 1097-1125, September.
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