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Additive Plausibility Characterizes the Supports of Consistent Assessments

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Abstract

We introduce three definitions. First, we let a "basement" be a set of nodes and actions that supports at least one assessment. Second, we derive from an arbitrary basement its implied "plausibility" (i.e. infinite-relative-likelihood) relation among the game's nodes. Third, we say that this plausibility relation is "additive" if it has a completion represented by the nodal sums of a mass function defined over the game's actions. This last construction is built upon Streufert (2012)'s result that nodes can be specified as sets of actions. Our central result is that a basement has additive plausibility if and only if it supports at least one consistent assessment. The result's proof parallels the early foundations of probability theory and requires only Farkas' Lemma. The result leads to related characterizations, to an easily tested necessary condition for consistency, and to the repair of a nontrivial gap in a proof of Kreps and Wilson (1982).

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  • Peter A. Streufert, 2012. "Additive Plausibility Characterizes the Supports of Consistent Assessments," University of Western Ontario, Departmental Research Report Series 20123, University of Western Ontario, Department of Economics.
    • Handle: RePEc:uwo:uwowop:20123
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    File URL: https://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=1253&context=economicsresrpt
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    References listed on IDEAS

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    1. Halpern, Joseph Y., 2010. "Lexicographic probability, conditional probability, and nonstandard probability," Games and Economic Behavior, Elsevier, vol. 68(1), pages 155-179, January.
    2. Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. Giacomo Bonanno, 2016. "AGM-consistency and perfect Bayesian equilibrium. Part II: from PBE to sequential equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1071-1094, November.
    2. Giacomo Bonanno, 2016. "AGM-consistency and perfect Bayesian equilibrium. Part II: from PBE to sequential equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1071-1094, November.
    3. Burkhard Schipper, 2014. "AGM-consistency and perfect Bayesian equilibrium. Part II: from PBE to sequential equilibrium," Working Papers 83, University of California, Davis, Department of Economics.

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    More about this item

    Keywords

    plausibility relation; additive representation; plausibility mass function; infinite relative likelihood;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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