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

Diversification, Convex Preferences and Non-Empty Core

We show, in the Choquet expected utility model, that preference for diversification, that is, convex preferences, is equivalent to a concave utility index and a convex capacity. We then introduce a weaker notion of diversification, namely ``sure diversification.'' We show that this implies that the core of the capacity is non-empty. The converse holds under concavity of the utility index. This property is shown to be equivalent to the notion of comonotone diversification\,; notion that we introduce in the paper. Finally, in the expected utility model, all these notions of diversification are equivalent and are represented by the concavity of the utility index.

Fairness under Uncertainty

Ever since its introduction by Foley (1967) and Varian (1974), the notion of fairness has been one of the most extensively used notion to evaluate allocations on an ethical basis. Whereas thereis an extensive literature on the efficiency properties of allocations in economies with uncertainty the concept of an envy-free allocation has not been widely studied in economies with uncertainty. We introduce two very natural notions of equity in an economy under uncertainty, namely ex ante and ex post equity, show they can contradict efficiency requirements. In particular, the set of ex ante efficient and ex post envy-free allocations may be empty. We nevertheless show that, under special circumstances, one may prove the existence of allocations that are both ex ante efficient and ex post envy-free. Such is the case, in particular, in an economy with individual risk and no aggregate risk.

Beliefs and Pareto Efficient Sets: A Remark

We show that, in a two-period economy with uncertainty in the second period, if an allocation is Pareto optimal for a given set of beliefs and remains optimal when these beliefs are changed, then the set of optimal allocations of the two economies must actually coincide. We identify equivalence classes of beliefs giving rise to the same set of Pareto optimal allocations.Beliefs, Pareto Optimality

Are beliefs a matter of taste? A case for Objective Imprecise Information

We argue, in the spirit of some of Jean-Yves Jaffray's work, that explicitly incorporating the information, however imprecise, available to the decision maker is relevant, feasible, and fruitful. In particular, we show that it can lead us to know whether the decision maker has wrong beliefs and whether it matters or not, that it makes it possible to better model and analyze how the decision maker takes into account new information, even when this information is not an event and finally that it is crucial when attempting to identify and measure the decision maker's attitude toward imprecise information.Decision under uncertainy;Objective Information;Belief Formation;Methodology of Decision Theory

Ambiguity aversion and the absence of wage indexation

This paper analyzes optimal wage contracting assuming agents are not subjective expectedutility maximizers but are, instead, ambiguity (or uncertainty) averse decision makers whomaximize Choquet expected utility. We show that such agents will choose not to include anyindexation coverage in their wage contracts even when inflation is uncertain, unless theperceived inflation uncertainty is high enough. Significantly, the exercise does not presume anyexogenous costs (e.g., transactions costs) of including indexation linksambiguity aversion; indexation

Are Beliefs a Matter of Taste ? A case for Objective Imprecise Information

We argue, in the spirit of some of Jean-Yves Jaffray's work, that explicitly incorporating the information, however imprecise, available to the decision marker is relevant, feasible and fruitful. In particular, we show that it can lead us to know whether the decision maker has wrong beliefs and whether it matters or not, that it makes it possible to better model and analyze how the decision maker takes into account new information, even when this information is not an event and finally that it is crucial when attempting to identify and measure the decision maker's attitude toward imprecise information.Beliefs, imprecision, information.

Ambiguity Aversion and Incompleteness of Financial Markets

It is widely thought that incomes risks can be shared by trading infinancial assets. But financial assets typically carry some riskidiosyncratic to them, hence, disposing incomes risk using financial assetswill involve buying into the inherent idiosyncratic risk. However, standardtheory argues that diversification would reduce the inconvenience ofidiosyncratic risk to arbitrarily low levels. This argument is less robustthan what standard theory leads us to believe: ambiguity aversion canexacerbate the tension between the two kinds of risks to the point thatclasses of agents may not want to trade some financial assets. Thus,theoretically, the effect of ambiguity aversion on financial markets is tomake the risk sharing opportunities offered by financial markets lesscomplete than it would be otherwise.incomplete markets; ambiguity aversion

An overview of economic applications of David Schmeidler`s models of decision making under uncertainty

This paper surveys some economic applications of the decision theoretic framework pioneered by David Schmeidler to model effects of ambiguity. We have organized the discussion principally around three themes: financial markets, contractual arrangements and game theory. The first section discusses papers that have contributed to a better understanding of financial market outcomes based on ambiguity aversion. The second section focusses on contractual arrangements and is divided into two sub-sections. The first sub-section reports research on optimal risk sharing arrangements, while in the second sub-section, discusses research on incentive contracts. The third section concentrates on strategic interaction and reviews several papers that have extended different game theoretic solution concepts to settings with ambiguity averse players. A final section deals with several contributions which while not dealing with ambiguity per se, are linked at a formal level, in terms of the pure mathematical structures involved, with Schmeidler`s models of decision making under ambiguity. These contributions involve issues such as, inequality measurement, intertemporal decision making and multi-attribute choice.Ellsberg Paradox, Ambiguity aversion, Uncertainty aversion

Fairness under Uncertainty

Ever since its introduction by Foley [1967] and Varian [1974], the notion of fairness has been one of the most extensively used notion to evaluate allocations on an ethical basis. Whereas there is an extensive literature on the efficiency properties of allocations in economies with uncertainty the concept of an envy-free allocation has not been widely studied in economies with uncertainty. We introduce two very natural notions of equity in an economy under uncertainty, namely ex ante and ex post equity, show they can contradict efficiency requirements. In particular, the set of ex ante efficient and ex post envy-free allocations may be empty. We nevertheless show that, under special circumstances, one may prove the existence of allocations that are both ex ante efficient and ex post envy-free. Such is the case, in particular, in an economy with individual risk and no aggregate risk.Fairness, uncerainty, envy