Reputation in Continuous-Time Games
研究了连续时间博弈中大型玩家（如政府）面对小型玩家（如家庭）时的声誉动态，通过布朗运动扭曲的公共信号分析均衡特征，发现小型玩家对行为类型的先验信念会引发丰富的均衡动态。
We study reputation dynamics in continuous-time games in which a large player (e.g., government) faces a population of small players (e.g., households) and the large player's actions are imperfectly observable. The major part of our analysis examines the case in which public signals about the large player's actions are distorted by a Brownian motion and the large player is either a normal type, who plays strategically, or a behavioral type, who is committed to playing a stationary strategy. We obtain a clean characterization of sequential equilibria using ordinary differential equations and identify general conditions for the sequential equilibrium to be unique and Markovian in the small players' posterior belief. We find that a rich equilibrium dynamics arises when the small players assign positive prior probability to the behavioral type. By contrast, when it is common knowledge that the large player is the normal type, every public equilibrium of the continuous-time game is payoff-equivalent to one in which a static Nash equilibrium is played after every history. Finally, we examine variations of the model with Poisson signals and multiple behavioral types.