Incomplete-Information Games in Large Populations with Anonymity

The paper provides mathematical foundations for modeling strategic interdependence with a continuum of agents where uncertainty has an aggregate component and an agent-speci?c component and the latter satis?es a conditional law of large numbers. This decomposition of uncertainty is implied by a condition of anonymity in beliefs, under which the agent in question considers the other agents? types to be essentially pairwise exchangeable. If there is also anonymity in payoff functions, all strategically relevant aspects of beliefs are contained in an agent?s macro beliefs about the cross-section distribution of the other agents?types. The paper also gives conditions under which a function assigning macro beliefs to types is compatible with the existence of a common prior. Key Words: Incomplete-information games, large populations, belief functions, common priors, exchangeability, conditional independence, conditional exact law of large numbers.

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