Articles

A Non-Minimal But Very Weak Axiomatization of Common Belief

L. Lismont, P. MONGIN

Artificial Intelligence

1994, vol. 70, pp.363-374

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)


Additive Representations of Non-Additive Measures and the Choquet Integral

I. GILBOA, D. Schmeidler

Annals of Operations Reseach

1994, vol. 51, pp.43-65

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)


Harsanyi's Aggregation Theorem - Multi-Profile Version and Unsettled Questions

P. MONGIN

Social Choice and Welfare

1994, vol. 11, pp.331-354

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)


Harsanyi's Aggregation Theorem states that if the individuals' as well as the moral observer's utility functions are von Neumann-Morgenstern, and a Pareto condition holds, then the latter function is affine in terms of the former. Sen and others have objected to Harsanyi's use of this result as an argument for utilitarianism. The present article proves an analogue of the Aggregation Theorem within the multi-profile formalism of social welfare functionals. This restatement and two closely related results provide a framework in which the theorem can be compared with well-known characterisations of utilitarianism, and its ethical significance can be better appreciated. While several interpretative questions remain unsettled, it is argued that at least one major objection among those raised by Sen has been answered

Infinite Histories and Steady Orbits in Repeated Games

I. GILBOA, D. Schmeidler

Games and Economic Behavior

1994, vol. 6, pp.370-399

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)


Introduction

P. MONGIN

Theory and Decision

1994, vol. 37, n°1, pp.1-6

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)


L'analyse de la variance à un facteur

M. TENENHAUS

Revue de Méthodologie et d'Analyse des Données

1994, n°6, pp.5-21

Départements : Economie et Sciences de la décision


L'optimisation est-elle un critère de rationalité individuelle?

P. MONGIN

Dialogue: Canadian Philosophical Review/Revue canadienne de philosophie

1994, vol. 33, pp.191-222

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)


Linear Measures, the Gini Index and the Income-Equality Tradeoff

E. Ben-Porath, I. GILBOA

Journal of Economic Theory

1994, vol. 64, pp.443-467

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)


On the Logic of Common Belief and Common Knowledge

L. Lismont, P. MONGIN

Theory and Decision

1994, vol. 37, pp.75-106

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)


The paper surveys the currently available axiomatizations of common belief (CB) and common knowledge (CK) by means of modal propositional logics. (Throughout, knowledge - whether individual or common - is defined as true belief.) Section 1 introduces the formal method of axiomatization followed by epistemic logicians, especially the syntax-semantics distinction, and the notion of a soundness and completeness theorem. Section 2 explains the syntactical concepts, while briefly discussing their motivations. Two standard semantic constructions, Kripke structures and neighbourhood structures, are introduced in Sections 3 and 4, respectively. It is recalled that Aumann's partitional model of CK is a particular case of a definition in terms of Kripke structures. The paper also restates the well-known fact that Kripke structures can be regarded as particular cases of neighbourhood structures. Section 3 reviews the soundness and completeness theorems proved w.r.t. the former structures by Fagin, Halpern, Moses and Vardi, as well as related results by Lismont. Section 4 reviews the corresponding theorems derived w.r.t. the latter structures by Lismont and Mongin. A general conclusion of the paper is that the axiomatization of CB does not require as strong systems of individual belief as was originally thought - only monotonicity has thus far proved indispensable. Section 5 explains another consequence of general relevance: despite the ''infinitary'' nature of CB, the axiom systems of this paper admit of effective decision procedures, i.e., they are decidable in the logician's sense

Positive dependence orderings and stopping times

B. Bassan, M. SCARSINI

Annals of the Institute of Statistical Mathematics

1994, vol. 46, pp.333-342

Départements : Economie et Sciences de la décision



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