Absorbing games with compact action spaces

J. Mertens, D. ROSENBERG, A. Neyman

Mathematics of Operations Research

mai 2009, vol. 34, n°2, pp.257-262

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

pas sous affiliation HEC

Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

H. Rue, S. Martino, N. CHOPIN

Journal of the Royal Statistical Society: Series B - Statistical Methodology

mars 2009, vol. 71, n°2, pp.319-392

Départements : Economie et Sciences de la décision

Mots clés : Approximate Bayesian inference, Gaussian Markov random fields, Generalized additive mixed models, Laplace approximation, Parallel computing, Sparse matrices, Structured additive regression models

Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged Approximate Bayesian inference Gaussian Markov random fields Generalized additive mixed models Laplace approximation Parallel computing Sparse matrices Structured additive regression models

Choix individuel et décision fondée sur l'expérience : une étude expérimentale


Revue Economique

2009, vol. 60, n°4

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

La plupart des résultats expérimentaux en théorie de la décision ont été obtenus dans un cadre où les options offertes aux individus sont parfaitement décrites en termes de conséquences mais également en termes de vraisemblance des événements. Ce type de décision peut être qualifié de décision fondée sur la description. Dans cet article, nous envisageons un contexte d'incertitude où la seule information disponible provient des réalisations observées de certains événements. Ce type de décision peut être qualifié de décision fondée sur l'expérience. Les études récentes sur la décision fondée sur l'expérience suggèrent que, dans ce cadre, les événements rares sont sous-pondérés par les individus et non surpondérés comme le suppose la grande majorité de la littérature. L'objectif de cet article expérimental est d'envisager dans quelle mesure les décisions fondées sur l'expérience diffèrent des décisions fondées sur la description.

Évolution de prix de référence du vendeur : une étude expérimentale sur le marché immobilier

R. Chenavaz, C. PARASCHIV

Revue Française du Marketing

mars 2009, n°221, pp.31-45

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

La prise de décision des consommateurs est souvent modélisée en intégrant un point de référence pour le prix. En étudiant le marché immobilier, nous nous interrogeront sur l'évolution du point de référence des vendeurs de biens immobiliers en fonction de l'évolution, favorable ou défavorable, du marché. Notre étude montre que le point de référence s'adapte plus rapidement sur un marché immobilier en hausse que sur un marché immobilier en baisse, que les vendeurs acceptent des prix inférieurs au prix de marché sur un marché en hausse alors qu'ils demandent des prix supérieurs au prix du marché sur un marché en baisse et que le prix d'achat a un rôle plus important sur un marché en baisse que sur un marché en hausse. Loss aversionProspect theoryReal estateReference pointAversion aux pertesImmobilierPoint de référenceProspect theory

Hessian orders and multinormal distributions

M. SCARSINI, A. Arlotto

Journal of Multivariate Analysis

novembre 2009, vol. 100, n°10, pp.2324-2330

Départements : Economie et Sciences de la décision

Mots clés : Hessian orders, Multivariate normal distribution, Convex cones, Dual space, Completely positive order

Several well known integral stochastic orders (like the convex order, the supermodular order, etc.) can be defined in terms of the Hessian matrix of a class of functions. Here we consider a generic Hessian order, i.e., an integral stochastic order defined through a convex cone HH of Hessian matrices, and we prove that if two random vectors are ordered by the Hessian order, then their means are equal and the difference of their covariance matrices belongs to the dual of HH. Then we show that the same conditions are also sufficient for multinormal random vectors. We study several particular cases of this general result

Informational externalities and emergence of consensus


Games and Economic Behavior

juillet 2009, vol. 66, n°2, pp.979-994

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

Mots clés : Studies, Externality, Economic models, Game theory

We study a general model of dynamic games with purely informational externalities. We prove that eventually all motives for experimentation disappear, and provide the exact rate at which experimentation decays. We also provide tight conditions under which players eventually reach a consensus. These results imply extensions of many known results in the literature of social learning and getting to agreement.

Informationally optimal correlation

O. Gossner, R. Laraki, T. TOMALA

Mathematical Programming

janvier 2009, vol. 116, n°1/2, pp.147-172

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

Mots clés : Correlation, Entropy, Repeated games

This papers studies an optimization problem under entropy constraints arising from repeated games with signals. We provide general properties of solutions and a full characterization of optimal solutions for 2 × 2 sets of actions. As an application we compute the minmax values of some repeated games with signals

Is It Always Rational to Satisfy Savage's Axioms?

I. GILBOA, A. Postlewaite, D. Schmeidler

Economics and Philosophy

novembre 2009, vol. 25, n°3, pp.285-297

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

This note argues that, under some circumstances, it is more rational not to behave in accordance with a Bayesian prior than to do so. The starting point is that in the absence of information, choosing a prior is arbitrary. If the prior is to have meaningful implications, it is more rational to admit that one does not have sufficient information to generate a prior than to pretend that one does. This suggests a view of rationality that requires a compromise between internal coherence and justification, similarly to compromises that appear in moral dilemmas. Finally, it is argued that Savage's axioms are more compelling when applied to a naturally given state space than to an analytically constructed one; in the latter case, it may be more rational to violate the axioms than to be BayesianStudies, Economic theory, Probability, Philosophy

Le problème dynamique de l'induction


Dialogue: Canadian Philosophical Review/Revue canadienne de philosophie

décembre 2009, vol. 48, n°4, pp.701-715

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

Living without state-independence of utilities


Theory and Decision

octobre 2009, vol. 67, n°4, pp.405-433

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

This article is concerned with the representation of preferences which do not satisfy the ordinary axioms for state-independent utilities. After suggesting reasons for not being satisfied with solutions involving state-dependent utilities, an alternative representation shall be proposed involving state-independent utilities and a situation-dependent factor. The latter captures the interdependencies between states and consequences. Two sets of axioms are proposed, each permitting the derivation of subjective probabilities, state-independent utilities, and a situation-dependent factor, and each operating in a different framework. The first framework involves the concept of a decision situation--consisting of a set of states, a set of consequences and a preference relation on acts; the probabilities, utilities and situation-dependent factor are elicited by referring to other, appropriate decision situations. The second framework, which is technically related, operates in a fixed decision situation; particular "subsituations" are employed in the derivation of the representation. Possible interpretations of the situation-dependent factor and the notion of situation are discussed.Studies, Decision making models, Decision theory