Incomplete‐information games in large populations with anonymity
研究了在连续代理人且不确定性分解为宏观和个体特定成分时，策略互动的理论基础，给出了代理人类型可交换性条件与匿名性下行为决定因素，并提供了函数与共同先验兼容的充要条件。
The paper provides theoretical foundations for models of strategic interdependence under uncertainty that have a continuum of agents and a decomposition of uncertainty into a macro component and an agent‐specific micro component, with a law of large numbers for the latter. This macro–micro decomposition of uncertainty is implied by a condition of exchangeability of agents' types, which holds at the level of the prior if and only if it also holds at the level of agents' beliefs, i.e., posteriors. Under an additional condition of anonymity in payoffs, agents' behaviors are fully determined by their beliefs about the cross‐section distribution of types and other macro variables, and by their beliefs about the cross‐section distribution of other agents' strategies. Any probability distribution over cross‐section distributions of types and other macro variables is compatible with a fully specified belief system, but not every function from types to such probability distributions is compatible with a common prior. The paper gives necessary and sufficient conditions for compatibility of such a function with a common prior.