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Revisiting log-linear learning: Asynchrony, completeness and payoff-based implementation


  • Marden, Jason R.
  • Shamma, Jeff S.


Log-linear learning is a learning algorithm that provides guarantees on the percentage of time that the action profile will be at a potential maximizer in potential games. The traditional analysis of log-linear learning focuses on explicitly computing the stationary distribution and hence requires a highly structured environment. Since the appeal of log-linear learning is not solely the explicit form of the stationary distribution, we seek to address to what degree one can relax the structural assumptions while maintaining that only potential function maximizers are stochastically stable. In this paper, we introduce slight variants of log-linear learning that provide the desired asymptotic guarantees while relaxing the structural assumptions to include synchronous updates, time-varying action sets, and limitations in information available to the players. The motivation for these relaxations stems from the applicability of log-linear learning to the control of multi-agent systems where these structural assumptions are unrealistic from an implementation perspective.

Suggested Citation

  • Marden, Jason R. & Shamma, Jeff S., 2012. "Revisiting log-linear learning: Asynchrony, completeness and payoff-based implementation," Games and Economic Behavior, Elsevier, vol. 75(2), pages 788-808.
  • Handle: RePEc:eee:gamebe:v:75:y:2012:i:2:p:788-808
    DOI: 10.1016/j.geb.2012.03.006

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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Sawa, Ryoji, 2014. "Coalitional stochastic stability in games, networks and markets," Games and Economic Behavior, Elsevier, vol. 88(C), pages 90-111.
    3. Carlos Alós-Ferrer & Nick Netzer, 2015. "Robust stochastic stability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 31-57, January.
    4. Carlos Alós-Ferrer & Nick Netzer, 2017. "On the convergence of logit-response to (strict) Nash equilibria," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 1-8, April.

    More about this item


    Potential games; Equilibrium selection; Distributed control;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis


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