Convergence and Stability of Coupled Belief-Strategy Learning Dynamics in Continuous Games
研究在连续博弈中，策略性玩家依赖信息平台学习未知参数时，信念与策略耦合学习动态的收敛性和稳定性，给出全局稳定不动点的充要条件及局部稳定性的充分条件。
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. Funding: Financial support from the Air Force Office of Scientific Research [Project Building Attack Resilience into Complex Networks], the Simons Institute [research fellowship], and a Michael Hammer Fellowship is gratefully acknowledged.