International Journal of Game Theory

, Volume 43, Issue 1, pp 13–24 | Cite as

How long to Pareto efficiency?



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.


Nash Equilibrium Payoff Function Communication Complexity Pareto Improvement Pareto Efficiency 



This work is part of the author’s Ph.D. thesis. The author wishes to thank his supervisor Sergiu Hart for his support and guidance and Noam Nisan for useful discussion. This research was partially supported by ERC Grant 0307950, and by ISF Grant 0397679.


  1. Arieli I, Babichenko Y (2011) Average testing and the efficient boundary. Discussion Paper 567, Center for the Study of Rationality, Hebrew University.Google Scholar
  2. Conitzer V, Sandholm T (2004) Communication complexity as a lower bound for learning in games. In: Brody CE (ed.) Machine Learning, Proceedings of the Twenty-First International Conference (ICML 2004), Banff, July 2004, ACM, New York, pp 185-192.Google Scholar
  3. Hart S, Mas Colell A (2003) Uncoupled dynamics do not lead to Nash equilibrium. Am Econ Rev 93:1830–1836CrossRefGoogle Scholar
  4. Hart S, Mas Colell A (2006) Stochastic uncoupled dynamics and Nash equilibrium. Games Econ Behav 57:286–303CrossRefGoogle Scholar
  5. Hart S, Mansour Y (2010) How long to equilibrium? The communication complexity of uncoupled equilibrium procedures. Games Econ Behav 69:107–126CrossRefGoogle Scholar
  6. Kushilevitz E, Nisan N (1997) Communication complexity. Cambridge University Press, CambridgeGoogle Scholar
  7. Marden JR, Young HP, Pao LY (2011) Achieving Pareto optimality through distributed learning, Economics series working papers, 557. University of Oxford, OxfordGoogle Scholar
  8. Pradelski B, Young HP (2010) Efficiency and equilibrium in trial and error learning, Economics series working papers, 480. University of Oxford, OxfordGoogle Scholar
  9. Saari DG, Simon CP (1978) Effective price mechanisms. Econometrica 46:1097–1125CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Computing and Mathematical SciencesCenter for the Mathematics of Information, California Institute of TechnologyPasadenaUSA

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