Articles scientifiques

Ambiguity and the Bayesian Approach

I. GILBOA, M. Marinacci

Advances in Economics and Econometrics: Theory and Applications

mai 2013, vol. 1

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

Awareness and equilibrium



mars 2013, vol. 190, n°5, pp.851-869

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

Mots clés : Logical omniscience, Formal representations of belief, Cognitive equilibrium, Awareness change, Doxastic actualism, Belief re-evaluation

There has been a recent surge of interest among economists in developing models of doxastic states that can account for some aspects of human cognitive limitations that are ignored by standard formal models, such as awareness. Epistemologists purport to have a principled reason for ignoring the question of awareness: under the equilibrium conception of doxastic states they favour, a doxastic state comprises the doxastic commitments an agent would recognise were he fully aware, so the question of awareness plays no role. The objective of this paper is to scrutinize this argument. A thesis underlying the argument, which we call the independence of doxastic commitments with respect to awareness, is identified, and examples are given where it appears to be violated. By considering these examples, one can get an idea of the price of accepting this thesis. On the one hand, one can escape the conclusion that the thesis is violated, but only at the expense of another principle espoused by all major formal models of belief, which we call constant doxastic rest; and abandoning this principle necessitates extensive revision of current models of belief. On the other hand, there are epistemologically valid reasons for thinking that the thesis fails to hold in the examples, which have to be rebutted if the thesis, and the equilibrium justification for ignoring the issue of awareness, are to be retained

Belief-free communication equilibria in repeated games


Mathematics of Operations Research

novembre 2013, vol. 38, n°4, pp.617-637

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

Mots clés : Repeated games, Incomplete information imperfect monitoring, Communication equilibrium

This paper considers a general model of repeated games with incomplete information and imperfect monitoring. We study belief-free communication equilibria (BFCE) defined as follows. Players communicate with a mediator who receives types and signals and recommends actions. A BFCE is a communication device such that all players have an incentive to play faithfully, irrespectively of their belief about the state. We characterize BFCE payoffs for any repeated game with incomplete information in terms of one-shot payoff functions, information, and signaling structure

Computational Aspects of Bayesian Spectral Density Estimation


Journal of Computational & Graphical Statistics

juillet 2013, vol. 22, n°3, pp.533-557

Départements : Economie et Sciences de la décision

Mots clés : FEXP, Long-memory processes, Sequential Monte Carlo

Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the nonsparse nature of the covariance matrix. We derive a fast approximation of the likelihood for such models. We propose to sample from the approximate posterior (i.e., the prior times the approximate likelihood), and then to recover the exact posterior through importance sampling. We show that the variance of the importance sampling weights vanishes as the sample size goes to infinity. We explain why the approximate posterior may typically be multimodal, and we derive a Sequential Monte Carlo sampler based on an annealing sequence to sample from that target distribution. Performance of the overall approach is evaluated on simulated and real datasets. In addition, for one real-world dataset, we provide some numerical evidence that a Bayesian approach to semiparametric estimation of spectral density may provide more reasonable results than its frequentist counterparts. The article comes with supplementary materials, available online, that contain an Appendix with a proof of our main Theorem, a Python package that implements the proposed procedure, and the Ethernet datase

Confidence and decision


Games and Economic Behavior

novembre 2013, vol. 82, pp.675-692

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

Mots clés : Confidence, Multiple priors, Confidence ranking, Cautiousness coefficient, Ambiguity

Many real-life decisions have to be taken on the basis of probability judgements of which the decision maker is not entirely sure. This paper develops a decision rule for taking such decisions, which incorporates the decision maker's confidence in his probability judgements according to the following maxim: the larger the stakes involved in a decision, the more confidence is required in a probability judgement for it to play a role in the decision. A formal representation of the decision maker's confidence is proposed and used to formulate a family of decision models conforming to this maxim. A natural member of this family is studied in detail. It is structurally simpler than other recent models of decision under uncertainty, which may make it easier to apply to practical decisions, whilst being axiomatically sound, permitting the separation of beliefs and tastes, and allowing comparative statics analysis of attitudes to choosing in the absence of confidence