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Hierarchies of Beliefs for Many Player Games

Author

Listed:
  • Kondiparthy, Venkata Tanay Kasyap

    (Warwick University)

Abstract

Mertens and Zamir (1985) first provided the universal type space construction for finite player games of incomplete information with a compact state space. Brandenburger and Dekel (1993) complemented it for a Polish state space. This paper extends the construction of Brandenburger and Dekel (1993) to games with infinitely many players for Harsanyi’s notion of a type. The extension is formulated by randomly drawing a countably infinite set of actual players from a continuum of potential players, represented by their labels in [0,1]. The random distribution of the countably infinite set of actual players almost surely converges to Lebesgue due to the Glivenko–Cantelli theorem. A coherent type is shown to induce beliefs over other player’s types and common knowledge of coherency closes the model of beliefs. Implications of dropping the Polish space assumption are discussed and an informal extension to measurable spaces is provided for future work. The formalisation provided here allows Harsanyi’s notion of type to be applied in classes of games with many players such as Morris and Shin (2001)

Suggested Citation

  • Kondiparthy, Venkata Tanay Kasyap, 2024. "Hierarchies of Beliefs for Many Player Games," Warwick-Monash Economics Student Papers 72, Warwick Monash Economics Student Papers.
    • Handle: RePEc:wrk:wrkesp:72
    as

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    File URL: https://warwick.ac.uk/fac/soc/economics/research/wmesp/manage/72_-_venkata_tanay_kasyap_kondiparthy.pdf
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    References listed on IDEAS

    as
    1. Stephen Morris & Hyun Song Shin, 2000. "Global Games: Theory and Applications," Cowles Foundation Discussion Papers 1275, Cowles Foundation for Research in Economics, Yale University.
    2. Peter Hammond & Yeneng Sun, 2008. "Monte Carlo simulation of macroeconomic risk with a continuum of agents: the general case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 303-325, August.
    3. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    4. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Higher Order Beliefs ; Universal Type Space ; Many Player Games JEL classifications: C70 ; D83;
    All these keywords.

    JEL classification:

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

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