We consider in discrete time, a general class of sequential stochastic dynamic games with asymmetric information with the following features. The underlying system has Markovian dynamics controlled by the agents' joint actions. Each agent's instantaneous utility depends on the current system state and the agents' joint actions. At each time instant each agent makes a private noisy observation of the current system state and the agents' actions in the previous time instant. In addition, at each time instant all agents have a common noisy observation of the current system state and their actions in the previous time instant. Each agent's actions are part of his private information. The objective is to determine Bayesian Nash Equilibrium (BNE) strategy profiles that are based on a compressed version of the agents' information and can be sequentially computed; such BNE strategy profiles may not always exist. We present an approach/methodology that achieves the above-stated objective, along with an instance of a game where BNE strategy profiles with the above-mentioned characteristics exist. We show that the methodology also works for the case where the agents have no common observations.
翻译:我们以离散的时间来考虑一个具有以下特征的、具有不对称信息的连续随机动态游戏的一般类别。 基础系统有由代理商联合行动控制的Markovian动态。 每个代理商的瞬间效用取决于当前的系统状态和代理商的联合行动。 每当每个代理商对当前的系统状态和代理商在前一瞬间的行动进行私下的吵闹观察时, 每个代理商都会对当前系统状态及其在前一瞬间的行动进行共同的吵闹观察。 每个代理商的行动是其私人信息的一部分。 目标是确定Bayesian Nash Equilibrium(BNE)战略概况, 其依据是该代理商信息的压缩版本, 可以按顺序计算; 这种BNE战略简介可能并不总是存在。 我们提出了一个实现上述目标的方法/ 方法, 以及一个具有上述特征的BNE战略简介存在的游戏实例。 我们显示该方法也适用于代理商没有共同观测结果的案件。