Incomplete-Information Games in Large Populations with Anonymity

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. The decomposition of uncertainty is implied by a condition of exchangeability of agents' types, which is imposed equivalently imposed at the level of the prior or at the level of beliefs, i.e., posteriors. Under an additional condition of anonymity in payoffs, agents' behaviors are fully determined by their macro beliefs about the cross-section distribution of types and by the cross-section distribution of other agents' strategies. Any probability distribution over cross-section distributions of types is admissible, but not every macro belief function is compatible with a common prior