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Incomplete-Information Games in Large Populations with Anonymity

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  • Martin F. Hellwig

    (Max Planck Institute for Research on Collective Goods, Bonn)

Abstract

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' behaviours are fully determined by their macro beliefs about the cross-section distribution of types and other macro variables and 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 macro belief function is compatible with a common prior. The paper gives necessary and sufficient conditions for compatibility of a macro belief function with a common prior.

Suggested Citation

  • Martin F. Hellwig, 2020. "Incomplete-Information Games in Large Populations with Anonymity," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2020_20, Max Planck Institute for Research on Collective Goods, revised 09 Mar 2021.
    • Handle: RePEc:mpg:wpaper:2020_20
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    Cited by:

    1. Chen, Enxian & Qiao, Lei & Sun, Xiang & Sun, Yeneng, 2022. "Robust perfect equilibrium in large games," Journal of Economic Theory, Elsevier, vol. 201(C).
    2. Hellwig, Martin, 2022. "Incomplete-information games in large populations with anonymity," Theoretical Economics, Econometric Society, vol. 17(1), January.
    3. Enxian Chen Bin Wu Hanping Xu, 2024. "The equilibrium properties of obvious strategy profiles in games with many players," Papers 2410.22144, arXiv.org.

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    More about this item

    Keywords

    Incomplete-information games; large populations; belief functions; common priors; exchangeability; conditional independence; conditional exact law of large numbers;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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