38 research outputs found
Updating Choquet Integrals , Consequentialism and Dynamic Consistency
No full textChoquet capacities have been used to represent decision makers’ beliefs in order to generalise the expected utility approach. Conditional capacities have to be defined for dynamic choice situations where information may modify the decision maker future beliefs. Several updating rules have been proposed in the literature. We derive them from a general approach based on conditional Choquet expectations. Conversely, depending on the updating rule adopted, the conditional Choquet integral can take different values. Conditional Choquet Expected Utility are derived from axioms on preferences. However, it is now well-known in decision theory that if preferences satisfy simultaneously dynamic consistency and consequentialism axioms their representation is restricted to classical Expected Utility. We show that the rule proposed by Chateauneuf, Kast and Lapied (2001) is the only one to satisfy dynamic consistency with a nonnecessary additive capacityConditional Choquet expectation; Conditional capacity; Updating rules; Choquet Expected Utility; Dynamic consistency; Consequentialism.
The value of information with neo-additive beliefs
No full textWhen individual beliefs are not Bayesian, economic agents may refuse further information about the uncertainty they are facing. Choquet decision makers in particular may be information averse. This note shows that, if the capacity is neo-additive, then the information value is necessarily positive
The value of information with neo-additive beliefs
No full textWhen individual beliefs are not Bayesian, economic agents may refuse further information about the uncertainty they are facing. Choquet decision makers in particular may be information averse. This note shows that, if the capacity is neo-additive, then the information value is necessarily positive
Assurance automobile et sélection adverse dans un modèle de Choquet
No full textInternational audienceL'article étudie la sélection adverse dans le cas de la demande d'assurance d'une automobile louée lorsque le critère de décision est une espérance de Choquet. L'approche adoptée de l'intégration de l'information à la décision d'assurance autorise l'utilisation d'une procédure d'induction à rebours pour déterminer l'action optimale ex ante, ce qui permet de retrouver les conclusions du modèle bayésien. En revanche, le rôle de l'ambiguïté peut être pris en compte par les capacités, ce qui n'est pas le cas avec les probabilités. Lorsque le décideur présente de l'aversion envers celle-ci, son comportement consiste à surestimer l'information si un accident s'est produit à la première étape et à la sous-estimer dans le cas contraire. The article studies adverse selection in the context of insurance demand for a rent car when the decision criterion is a Choquet expectation. Our approach of integrating information to the insurance decision is able to implement a backward induction procedure to determine the optimal action undertaken ex ante. It allows to obtain the same conclusion than the bayesian model. However, the role of ambiguity may be take into account since we use capacities, rather than probabilities, to represent individual's beliefs. If the decision maker is ambiguity averse, she overweights the information if an accident has occurred at the first stage and under-weights it in the opposite case
CONSISTENT DYNAMICE CHOICE AND NON-EXPECTED UTILITY PREFERENCES
No full textPursuing works from Sarin and Wakker (1998), we study how NonExpected Utility models could be consistently applied to multi-stage decision problems. Concerning multiple priors model, we remove the argument that dynamic consistency, consequentialism and model consistency (sequential consistency in Sarin and Wakker (1998)) can all be preserved. Like Choquet expected utility, deviation of expected utility is only allowed over the final stage. Moreover, it's proved for the two models that if we also assume reduction of compound acts, then an expected utility representation exists in all stages.Choquet Expected Utility, Multiple Priors, Sequential Choice, Dynamic Consistency, Consequentialism, Reduction of Compound Acts.
Choquet expected utility with affine capacities: Choquet expected utility with affine capacities
No full textHumanities and Social Sciences/Economies and financesJournal articlesInternational audienceThis paper studies decisions under ambiguity when attention is paid to extreme outcomes. In a purely subjective framework, we propose an axiomatic characterization of affine capacities, which are Choquet capacities consisting in an affine transformation of a subjective probability. Our main axiom restricts the well-known Savage’s Sure-Thing Principle to a change in a common intermediate outcome. The representation result is then an affine combination of the expected utility of the valued act and its maximal and minimal utilities
Dynamic adverse selection with the best and the worst in mind
No full textInternational audienceThis paper analyzes a dynamic adverse selection market where buyers hold ambiguous beliefs about seller quality, modeled using neo-additive Choquet capacities and updated via optimistic, pessimistic, and Generalized Bayesian rules. First, we show that the choice of updating heuristic has a direct and systematic effect on the severity of adverse selection. While the optimistic and pessimistic rules invariably mitigate or amplify the problem, respectively, the Generalized Bayesian rule's impact is conditional, its trajectory toward collapse, efficiency, or a stable partial market depending on a persistent 'tug-of-war' between the buyer's static ambiguity attitude and the evolving probabilistic evidence. Our second main finding is that these immediate effects compound over time, leading to fundamentally different market trajectories. The pessimistic rule can drive the market to complete collapse, the optimistic rule can foster full participation, and the Generalized Bayesian path depends on the interplay between the buyer's attitude and the evolving evidence. We further analyze how baseline ambiguity and ambiguity aversion modulate these dynamics, uncovering a complex role for ambiguity in shaping the rate of market evolution
A note on "Re-examining the law of iterated expectations for Choquet decision makers"
No full textThis note completes the main result of [Zimper A., (2010) Re-examining the law of iterated expectations for Choquet decision makers. Theory and decision, DOI 10.1007/s11238-010-9221-8], by showing that additional conditions are needed in order the law of iterated expectations to hold true for Choquet decision makers. Due to the comonotonic additivity of Choquet expectations, the equation E[f; (d!)] = E[E[f(!i;j); (Ai;jjAi)]; (Ai)]; is valid only when the act f is comonotonic with its dynamic form, that we name "conditional certainty equivalent act"
Atemporal non-expected utility preferences, dynamic consistency and consequentialism
No full textInternational audienceThis note studies conditions which allow to maintain a non-expected utility representation (Max-min expected utility and Choquet expected utility), dynamic consistency and consequentialism in an atemporal and purely subjective framework. By contrast with a dynamic set-up, where consistency can be reached with non-expected utility models, we show that both Maxmin expected utility and Choquet expected utility degenerate into an expected utility representation
Dynamically consistent CEU preferences on -convex events
No full textInternational audienceWe give an axiomatic foundation to the updating rule proposed by Sarin and Wakker [Sarin, R., Wakker, P.P., 1998a. Revealed likelihood and knightian uncertainty. Journal of Risk and Uncertainty 16, 223–250] for CEU preferences. This rule is dynamically consistent but non-consequentialist, since forgone consequences are relevant for conditioning. Whereas it does not work universally, but only when counterfactuals outcomes are better and/or worse than the ones resulting on the conditioning event, the rule has many interesting features, since it is able to describe Ellsberg-type preferences together with a recursive structure of the criterion
