Articles

A Note on Affine Aggregation

P. MONGIN

Economics Letters

1995, vol. 47, pp.177-183

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


If a vector-valued function has convex range and one of its components is related to the others by a Pareto-like condition, that component must be affine w.r.t. the others; sign restrictions on the coefficients follow from suitably strengthening the unanimity condition. The theorem is applied to social choice and decision theories

Aggregation of Semi-Orders: Intransitive Indifference Makes a Difference

I. GILBOA, R. Lapson

Economic Theory

1995, vol. 5, pp.109-126

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


Belief Closure - A Semantics of Common Knowledge for Modal Propositional Logic

L. Lismont, P. MONGIN

Mathematical Social Sciences

1995, vol. 30, pp.127-153

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


The paper investigates the relations between iterate and fixed-point accounts of common belief and common knowledge, using the formal tools of epistemic modal logic. Its main logical contribution is to introduce and axiomatize the following (fixed-point) notion of common belief. We first define a proposition to be belief-closed if everybody believes it in every world where it is true. We then define a proposition to be common belief in a world if it is implied by a belief-closed proposition that everybody believes in that world. Using the belief closure semantics of common belief, the paper proves soundness and completeness theorems for modal logics of varying strength. The weakest system involves a monotonicity assumption on individual belief; the strongest system is based on S5. Axiomatizations of common knowledge are secured by adding the truth axiom to any system. The paper also discusses anticipations of the belief closure semantics in the economic and game-theoretic literatures

Canonical Representation of Set Functions

I. GILBOA, D. Schmeidler

Mathematical Methods of Operations Research

1995, vol. 20, pp.197-212

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


Case-Based Decision Theory

I. GILBOA, D. Schmeidler

Quarterly Journal of Economics

1995, vol. 110, pp.605-639

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


Comportements individuels devant le risque et distorsion des probabilités

M. ABDELLAOUI

Revue d'Economie Politique

1995, vol. 105, n°1, pp.157-178

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


Consistent Bayesian Aggregation

P. MONGIN

Journal of Economic Theory

1995, vol. 66, pp.313-351

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


We investigate the aggregation of first nonatomic probabilities and second Savagean orderings, subject to the following consistency constraints: (i) the aggregate is a subjective probability or a Savagean ordering, respectively; and (ii) it satisfies the Pareto principle. Aggregation is viewed here as a single-profile exercise. We show that affine rules are the only solutions to the problem of aggregating nonatomic probabilities. Assuming weak Pareto conditions and technical restrictions, we show that dictatorial rules are the only solutions to the problem of aggregating Savagean orderings. No solution exists when strong Pareto replaces weaker conditions. Without technical restrictions of affine independence, nontrivial solutions may exist

Credible Equilibria in Games with Changing Utility

J. Ferreira, I. GILBOA, M. Maschler

Games and Economic Behavior

1995, vol. 10, pp.284-317

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


Finite exchangeability and linear regression

M. SCARSINI, B. Bassan

Statistics & Probability Letters

1995, vol. 23, pp.105-110

Départements : Economie et Sciences de la décision


On the value of information in multi-agent decision theory

M. SCARSINI, B. Bassan

Journal of Mathematical Economics

1995, vol. 24, n°6, pp.557-576

Départements : Economie et Sciences de la décision


Several agents, each with his own opinion (probability measure), make decisions in order to maximize their expected utility. A super partes person, 'the chief', releases information with the goal of maximizing a social expected utility, which is an increasing function of the agents' utilities. Additional bits of information are individually beneficial to each agent, but might be socially detrimental if the social utility is concave and therefore diversification is valuable. In this paper, information is modeled by filtrations on a suitable probability space, and the problem of establishing how much information ought to be released is tackled. Two situations are examined, in which the chief either updates or does not update her opinion


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