Characterizing the common prior assumption.
type: Item
instance of: scholarly article
title: Characterizing the common prior assumption.
zbMATH Open document ID: 1042.91062
author: Joseph Y. Halpern
published in: Journal of Economic Theory
publication date: 2003-04-02T00:00:00Z
review text: This paper provides a thorough theoretical investigation on the logical characterizations of the Common Prior Assumption (CPA). CPA has played a prominent role in economic theory, its essential meaning being that differences in beliefs among agents can be completely explained by differences in information they received. Using classical tools from modal logic, Joseph Halpern gives two different characterizations of CPA and compares them to those existing in the economics literature. The first CPA characterization is based on frame distinguishability, a concept closer to the notions typically considered in the economics literature, the results obtained for CPA frame distinguishability being similar to those already existing ones. In particular, the paper shows that finite frames (actually, finite spaces) that satisfy the CPA can be distinguished from those that do not, in terms of disagreements in expectation. However, it is also proved that there exist no formulas in the defined language which can distinguish infinite spaces satisfying the CPA, from those spaces that do not. A second approach to CPA characterization is based on finding a sound and complete axiomatization. In the proposed axiom system, the key axiom involves disagreements in expectation. Since the axiomatization is proved to be sound and complete both for the finite and infinite case, this logical language is too weak to distinguish finite and infinite spaces. This phenomenon is frequently met in various aspects of (fundamental) mathematics. Essentially, the result obtained says that in economics there exist ``nonstandard'' models that satisfy all the properties of the CPA expressible in the considered axiomatized language, despite the fact that these models do not satisfy the CPA (similarly to the nonstandard models of the real numbers that satisfy all the properties of the reals). Thus the two approaches characterizing the CPA behave quite differently in the case of infinite spaces. The answer to th…
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 91B44
Mathematics Subject Classification ID: 91A18
Mathematics Subject Classification ID: 91B02
Mathematics Subject Classification ID: 03B42
Mathematics Subject Classification ID: 03B45
zbMATH DE Number: 1891522
zbMATH Keywords: Common Prior Assumption (CPA)
zbMATH Keywords: CPA characterizations
zbMATH Keywords: theory of economics
zbMATH Keywords: agent beliefs
zbMATH Keywords: frame distinguishability
zbMATH Keywords: CPA finite frames disagreements in expectation
zbMATH Keywords: CPA logical system axiomatization
zbMATH Keywords: sound and complete axiom system for CPA
MaRDI profile type: Publication
OpenAlex ID: W2018618672
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DOI: 10.1006/JETH.2002.2925
description: scientific article; zbMATH DE number 1891522