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

• Main Authors: Wu, Manxi, Amin, Saurabh, Ozdaglar, Asuman
• Format: Journal Article
• Language: English
• Published: 11-06-2022
• Subjects: Computer Science - Multiagent Systems
• DOI: 10.48550/arxiv.2206.05637

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.