论文标题
具有自适应策略的多代理贝叶斯学习：融合与稳定性
Multi-agent Bayesian Learning with Adaptive Strategies: Convergence and Stability
论文作者
论文摘要
我们研究由战略代理人诱导的学习动力学，他们反复玩具有与回报相关的参数的游戏。在每个步骤中，信息系统都根据玩家的策略来估算参数的信念分布，并使用贝叶斯规则实现了回报。玩家通过考虑基于更新的信念的平衡策略或最佳响应策略来调整策略。我们证明，信念和策略会以概率1的范围融合到固定点。我们还提供了保证固定点的本地和全球稳定性的条件。任何固定点信念都始终估算给定固定点策略概况的收益分布。但是，并不能保证融合到完整的信息NASH平衡。我们提供了足够且必要的条件，在该条件下，固定点信念恢复未知参数。即使参数学习不完整，我们还为收敛提供了足够的条件，以完成信息均衡。
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.
