Games with imperfectly observable actions in continuous time

• 成果类型: Article
• 署名作者: Sannikov, Yuliy
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.1111/j.1468-0262.2007.00795.x
• 发表日期: 2007
• 页码: 1285-1329
• 关键词: Efficiency

摘要

This paper investigates a new class of two-player games in continuous time, in which the players' observations of each other's actions are distorted by Brownian motions. These games are analogous to repeated games with imperfect monitoring in which the players take actions frequently. Using a differential equation, we find the set epsilon(r) of payoff pairs achievable by all public perfect equilibria of the continuous-time game, where r is the discount rate. The same differential equation allows us to find public perfect equilibria that achieve any value pair on the boundary of the set epsilon(r). These public perfect equilibria are based on a pair of continuation values as a state variable, which moves along the boundary of epsilon(r) during the course of the game. In order to give players incentives to take actions that are not static best responses, the pair of continuation values is stochastically driven by the players' observations of each other's actions along the boundary of the set epsilon(r).