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

TL;DR

This paper introduces a coupled belief-strategy learning dynamics for continuous games, analyzing convergence, stability, and conditions for equilibrium, integrating Bayesian belief updates with strategic adjustments.

Contribution

It presents a novel framework combining Bayesian belief learning with strategy updates, providing convergence analysis and stability conditions for fixed points in continuous games.

Findings

Conditions for global stability of fixed points

Sufficient conditions for local stability

Characterization of long-term outcomes in belief-strategy learning

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's 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.