Incomplete-information games in large populations with anonymity

• 成果类型: Article
• 署名作者: Hellwig, Martin F.
• 署名单位: Max Planck Society
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE4066
• 发表日期: 2022-01-01
• 页码: 461-506
• 关键词: Incomplete-information games; large populations; belief functions; common priors; exchangeability; conditional independence; conditional exact law of large numbers; C70; D82; D83

摘要

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.