Additive Plausibility Characterizes the Supports of Consistent Assessments

Peter Streufert

No 20123, University of Western Ontario, Departmental Research Report Series from University of Western Ontario, Department of Economics

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).

Keywords: plausibility relation; additive representation; plausibility mass function; infinite relative likelihood (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
Date: 2012
New Economics Papers: this item is included in nep-gth and nep-mic
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Citations: View citations in EconPapers (3)

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