Beliefs and Dynamic Consistency,

In this chapter, we adopt the decision theoretic approach to the representation and updating of beliefs. We take up this issue and propose a reconsideration of Hammond's argument. After reviewing the argument more formally, we propose a weaker notion of dynamic consistency. We observe that this notion does not imply the full fledged sure thing principle thus leaving some room for models that are not based on expected utility maximization. However, these models still do not account for ''imprecision averse" behavior such as the one exhibited in Ellsberg experiment and that is captured by non-Bayesian models such as the multiple prior model. We therefore go on with the argument and establish that such non-Bayesian models possess the weak form of dynamic consistency when the information considered consists of a reduction in imprecision (in the Ellsberg example, some information about the proportion of Black and Yellow balls)R. Arena and A. Festré

Decisions with conflicting and imprecise information

The most usual procedure when facing decisions in complex settings consists in consulting experts, aggregating the information they provide, and deciding on the basis of this aggregated information. We argue that such a procedure entails a substantial loss, insofar as it precludes the possibility to take into account simultaneously the decision maker's attitude towards conflict among experts and her attitude towards imprecision of information. We propose to consider directly how a decision maker behaves when using information coming from several sources. We give an axiomatic foundation for a decision criterion that allows to distinguish on a behavioral basis the decision maker's attitude towards imprecision and towards conflict.Decisions with multiple sources of information. Conflict aversion. Imprecision aversion.

Decision Making with Imprecise Probabilistic Information

We develop an axiomatic approach to decision under uncertainty that explicitly takes into account the information available to the decision maker. The information is described by a set of priors and a reference prior. We define a notion of imprecision for this informational setting and show that a decision maker who is averse to information imprecision maximizes the minimum expected utility computed with respect to a subset of the set of initially given priors. The extent to which this set is reduced can be seen as a measure of imprecision aversion. This approach thus allows a lot of flexibility in modelling the decision maker attitude towards imprecision. In contrast, applyingGilboa-Schmeidler [1989] maxmin criterion to the initial set of priors amounts to assuming extreme pessimism.Uncertainty, Decision, Multiple Priors

Decision Making with Imprecise Probabilistic Information.

We develop an axiomatic approach to decision under uncertainty that explicitly takes into account the information available to the decision maker. The information is described by a set of priors and a reference prior. We define a notion of imprecision for this informational setting and show that a decision maker who is averse to information imprecision maximizes the minimum expected utility computed with respect to a subset of the set of initially given priors. The extent to which this set is reduced can be seen as a measure of imprecision aversion. This approach thus allows a lot of flexibility in modelling the decision maker attitude towards imprecision. In contrast, applying Gilboa and Schmeidler (1989) maxmin criterion to the initial set of priors amounts to assuming extreme pessimism.Uncertainty; Decision; Multiple Priors

Representation and aggregation of preferences under uncertainty

We axiomatize in the Anscombe–Aumann setting a wide class of preferences called rank-dependent additive preferences that includes most known models of decision under uncertainty as well as state dependent versions of these models. We prove that aggregation is possible and necessarily linear if and only if (society's) preferences are uncertainty neutral. The latter means that society cannot have a non-neutral attitude toward uncertainty on a subclass of acts. A corollary to our theorem is that it is not possible to aggregate multiple prior agents, even when they all have the same set of priors. A number of ways to restore the possibility of aggregation are then discussed.Aggregation; Uncertainty

On the impossibility of preference aggregation under uncertainty

We provide a general theorem on the aggregation of preferences under uncertainty. We study, in the Anscombe-Aumann setting a wide class of preferences, that includes most known models of decision under uncertainty (and state-dependent versions of these models). We prove that aggregation is possible and necessarily linear if (society's) preferences are "smooth". The latter means that society cannot have a non-neutral attitude towards uncertainty on a subclass of acts. A corollary to our theorem is that it is not possible to aggregate maxmin expected utility maximizers, even when they all have the same set of priors. We show that dropping a weak notion of monotonicity on society's preferences allows one to restore the possibility of aggregation of non-smooth preferences.Aggregation, Harsanyi, uncertainty, multiple priors.

Croyances et apprentissage en présence d'ambiguïté et de contingences non anticipées

L'objectif principal du projet était d'étendre le cadre Bayésien, modèle standard en économie pour la formalisation de l'incertitude, des croyances, de l'apprentissage, de l'information...; modèle qui conduit à des prédictions fortes et parfois peu réalistes en économie théorique. Or ce cadre Bayésien est extrêmement restrictif et ne permet pas de prendre en compte de nombreux comportements observés. Le projet présenté ici, en associant économistes, mathématiciens et informaticiens, avait pour but de tenter de bâtir un cadre formel non - Bayésien cohérent en exploitant les points de vue propres à chaque discipline. Plus particulièrement, trois thèmes ont été explorés. Dans le thème, formalisation de l'ambiguïté et impact sur les comportements individuels, des modèles de représentation des préférences individuelles dans l'incertain ont été développés, modèles qualitatifs et quantitatifs. Notamment une « mesure objective de l'ambiguïté » a été proposée permettant de définir une notion d'aversion à l'ambiguïté faisant le parallèle avec l'aversion au risque. Des applications économiques ont permis de montrer que tenir compte de cette aversion à l'ambiguïté modifiait sensiblement l'analyse des échanges en situation d'incertitude. Dans le thème, révision des croyances, qui de façon large abordait les problèmes de séquentialité, des progrès sensibles ont été obtenus. D'une part, il a été prouvé que des modèles de décision qualitative se prêtaient à la programmation dynamique au même titre que le modèle Bayésien. D'autre part des règles de révision des croyances ont été identifiées qui permettent d'éviter des comportements irrationnels. Une tentative opérationnelle d'amender la programmation dynamique pour éliminer le choix de stratégies dominées a été explorée. Enfin, une théorie de la révision des croyances croisées dans une situation multi – agents a été ébauchée. Dans le thème formalisation des contingences non anticipées et des processus cognitifs du décideur, des travaux théoriques et des expériences ont permis de mieux cerner le problème des préférences incomplètes. L'importation des outils de la théorie du choix dans l'incertain dans l'analyse multicritère a permis de proposer de nouvelles techniques d'agrégation.Croyances ; ambiguïté ; apprentissage ; décision

Transport, health and climate change: Deciding on the optimal policy

Transport generates many externalities, some related to atmospheric pollution. In this paper, we focus on two: greenhouse gases, and local pollution. In the search for optimal transport policies, these two externalities have usually been analysed separately. Here, we study them jointly, in a sequential decision-making model. Our model allows for the irreversibility of the policies undertaken, as well as the possibility of a progressive reduction of uncertainties with the arrival of information. We find that when both sources of externalities are analysed jointly, structural measures enabling private transport requirements to be reduced are identified as being more advantageous economically than technological measures to reduce emissions of pollutants. We illustrate the usefulness of a joint analysis of externalities with two examples: tax measures on cars and housing policy.climate change; model of decision-making under uncertainty; irreversibilities; transport policy

Multiplayer belief revision

One main topic of the epistemic program of game theory deals with the value of information. To study this question in a broad context, one needs to adapt some of the tools used in multiplayer epistemic logic. A hierarchical belief structure is introduced both in a syntactical and semantical framework. In the same framework, a generalized notion of message is characterized by its content and its status. For a given message, a multiplayer belief revision rule that transforms any initial belief structure into a final belief one is designed. A representation theorem relates syntactical axioms to the belief revision rule.Belief revision, message, epistemic logic.

Beliefs and Dynamic Consistency,

In this chapter, we adopt the decision theoretic approach to the representation and updating of beliefs. We take up this issue and propose a reconsideration of Hammond's argument. After reviewing the argument more formally, we propose a weaker notion of dynamic consistency. We observe that this notion does not imply the full fledged sure thing principle thus leaving some room for models that are not based on expected utility maximization. However, these models still do not account for ''imprecision averse" behavior such as the one exhibited in Ellsberg experiment and that is captured by non-Bayesian models such as the multiple prior model. We therefore go on with the argument and establish that such non-Bayesian models possess the weak form of dynamic consistency when the information considered consists of a reduction in imprecision (in the Ellsberg example, some information about the proportion of Black and Yellow balls