Additive Plausibility Characterizes the Supports of Consistent Assessments
AbstractWe 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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Bibliographic InfoPaper provided by University of Western Ontario, Department of Economics in its series UWO Department of Economics Working Papers with number 20123.
Date of creation: 2012
Date of revision:
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plausibility relation; additive representation; plausibility mass function; infinite relative likelihood;
Find related papers by JEL classification:
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-12-06 (All new papers)
- NEP-GTH-2012-12-06 (Game Theory)
- NEP-MIC-2012-12-06 (Microeconomics)
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- Halpern, Joseph Y., 2010. "Lexicographic probability, conditional probability, and nonstandard probability," Games and Economic Behavior, Elsevier, vol. 68(1), pages 155-179, January.
- Giacomo Bonanno, 2014. "AGM-consistency and perfect Bayesian equilibrium. Part II: from PBE to sequential equilibrium," Working Papers 141, University of California, Davis, Department of Economics.
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