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Convergence and Stability of Coupled Belief-Strategy Learning Dynamics in Continuous Games

Author

Listed:
  • Manxi Wu

    (School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14850)

  • Saurabh Amin

    (Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Asuman Ozdaglar

    (Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

We propose a learning dynamics to model how strategic agents repeatedly play a continuous game while relying on an information platform to learn an unknown payoff-relevant parameter. In each time step, the platform updates a belief estimate of the parameter based on players’ strategies and realized payoffs using Bayes’ rule. Then, players adopt a generic learning rule to adjust their strategies based on the updated belief. We present results on the convergence of beliefs and strategies and the properties of convergent fixed points of the dynamics. We obtain sufficient and necessary conditions for the existence of globally stable fixed points. We also provide sufficient conditions for the local stability of fixed points. These results provide an approach to analyzing the long-term outcomes that arise from the interplay between Bayesian belief learning and strategy learning in games and enable us to characterize conditions under which learning leads to a complete information equilibrium.

Suggested Citation

  • Manxi Wu & Saurabh Amin & Asuman Ozdaglar, 2025. "Convergence and Stability of Coupled Belief-Strategy Learning Dynamics in Continuous Games," Mathematics of Operations Research, INFORMS, vol. 50(1), pages 459-481, February.
    • Handle: RePEc:inm:ormoor:v:50:y:2025:i:1:p:459-481
    DOI: 10.1287/moor.2022.0161
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