Multi-agent Bayesian Learning with Adaptive Strategies: Convergence and Stability
This addresses strategic learning in multi-agent systems, but it is incremental as it builds on existing Bayesian learning frameworks.
The paper tackles the problem of multi-agent learning in games with unknown parameters, proving that beliefs and strategies converge to a fixed point with probability 1 and providing stability conditions, but convergence to a complete information Nash equilibrium is not always guaranteed.
We study learning dynamics induced by strategic agents who repeatedly play a game with an unknown payoff-relevant parameter. In each step, an information system estimates a belief distribution of the parameter based on the players' strategies and realized payoffs using Bayes' rule. Players adjust their strategies by accounting for an equilibrium strategy or a best response strategy based on the updated belief. We prove that beliefs and strategies converge to a fixed point with probability 1. We also provide conditions that guarantee local and global stability of fixed points. Any fixed point belief consistently estimates the payoff distribution given the fixed point strategy profile. However, convergence to a complete information Nash equilibrium is not always guaranteed. We provide a sufficient and necessary condition under which fixed point belief recovers the unknown parameter. We also provide a sufficient condition for convergence to complete information equilibrium even when parameter learning is incomplete.