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Most games violate the common priors doctrine

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  • Yaw Nyarko

Abstract

The type of a player in a game describes the beliefs of that player about the types of others. We show that the subset of vectors of such player‐type beliefs which obey the consistency condition sometimes called the Harsanyi doctrine is of Lebesgue measure zero. Furthermore, as the number of players becomes large the ratio of the dimension Harsanyi‐consistent beliefs to the set of all beliefs tends to zero.

Suggested Citation

  • Yaw Nyarko, 2010. "Most games violate the common priors doctrine," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 189-194, March.
    • Handle: RePEc:bla:ijethy:v:6:y:2010:i:1:p:189-194
    DOI: 10.1111/j.1742-7363.2009.00129.x
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    References listed on IDEAS

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    1. Hellman, Ziv & Samet, Dov, 2012. "How common are common priors?," Games and Economic Behavior, Elsevier, vol. 74(2), pages 517-525.
    2. Nyarko, Yaw, 1990. "Bayesian Rationality And Learning Without Common Priors," Working Papers 90-45, C.V. Starr Center for Applied Economics, New York University.
    3. John C. Harsanyi, 1968. "Games with Incomplete Information Played by "Bayesian" Players Part II. Bayesian Equilibrium Points," Management Science, INFORMS, vol. 14(5), pages 320-334, January.
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    1. Hellman, Ziv & Samet, Dov, 2012. "How common are common priors?," Games and Economic Behavior, Elsevier, vol. 74(2), pages 517-525.
    2. Halpern, Joseph Y. & Kets, Willemien, 2015. "Ambiguous language and common priors," Games and Economic Behavior, Elsevier, vol. 90(C), pages 171-180.
    3. Guilhem Lecouteux, 2018. "Bayesian game theorists and non-Bayesian players," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 25(6), pages 1420-1454, November.

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