Attitude toward information and learning under multiple priors

This paper studies learning under multiple priors by characterizing the decision maker's attitude toward information. She is incredulous if she integrates new information with respect to only those measures that minimizes the likelihood of the new information and credulous if she uses the maximum likelihood procedure to update her priors. Both updating rules expose her to dynamic inconsistency. We explore different ways to resolve this problem. One way consists to assume that the decision maker's attitude toward information is not relevant to characterize conditional preferences. In this case, we show that a necessary and sufficient condition, introduced by [Epstein L. and Schneider M., 2003. Recursive multiple priors. Journal of Economic Theory 113, 1-31], is the rectangularity of the set of priors. Another way is to extend optimism or pessimism to a dynamic set-up. A pessimistic (max-min expected utility) decision maker will be credulous when learning bad news but incredulous when learning good news.Conversely, an optimistic (max-max expected utility) decision maker will be credulous when learning good news but incredulous when learning bad news. It allows max-min (or max-max) expected utility preferences to be dynamically consistent but it violates consequentialism because conditioning works with respect to counterfactual outcomes. The implications of our findings when the set of priors is the core of a non-additive measure are explored.Multiple priors ; Learning ; Dynamic consistency ; Consequentialism ; Attitude toward information

Dynamically consistent CEU preferences

We give an axiomatic foundation to the updating rule proposed by [Sarin, R. and Wakker, P. P. (1998). Revealed likelihood and knightian uncertainty. Journal of Risk and Uncertainty 16(3):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 Ellsbergtype preferences together with a recursive structure of the criterion

Updating Choquet Integrals , Consequentialism and Dynamic Consistency

Choquet 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.

Consistent dynamic choice and non-expected utility preferences

This paper studies the application of the two most popular non-expected utility (NEU) models -Choquet Expected Utility (CEU) and Maximin Expected Utility (CEU)- to dynamic choice situations in a purely subjective framework. We give an appropriate version of the reduction of compound acts axiom, that states the equivalence between a static and a dynamic choice situation. We show that if consequentialism -only those consequences that can be reached do matter- is additionally assumed, then a monotonic constant linear representation degenerate into expected utility. We envisage two different ways to resolve this problem for the cases where the representation is a CEU or a MEU one. One way consists to weaken the reduction of compound acts axiom, which does not hold on all events. Another way is to relax consequentialism. Then we axiomatically characterize an updating rule for both approaches allowing recursion in several cases

Attitude toward information and learning under multiple priors

This paper studies learning under multiple priors by characterizing the decision maker's attitude toward information. She is incredulous if she integrates new information with respect to only those measures that minimizes the likelihood of the new information and credulous if she uses the maximum likelihood procedure to update her priors. Both updating rules expose her to dynamic inconsistency. We explore different ways to resolve this problem. One way consists to assume that the decision maker's attitude toward information is not relevant to characterize conditional preferences. In this case, we show that a necessary and sufficient condition, introduced by [Epstein L. and Schneider M., 2003. Recursive multiple priors. Journal of Economic Theory 113, 1-31], is the rectangularity of the set of priors. Another way is to extend optimism or pessimism to a dynamic set-up. A pessimistic (max-min expected utility) decision maker will be credulous when learning bad news but incredulous when learning good news.Conversely, an optimistic (max-max expected utility) decision maker will be credulous when learning good news but incredulous when learning bad news. It allows max-min (or max-max) expected utility preferences to be dynamically consistent but it violates consequentialism because conditioning works with respect to counterfactual outcomes. The implications of our findings when the set of priors is the core of a non-additive measure are explored

Choquet expected utility with affine capacities: Choquet expected utility with affine capacities

Humanities 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

Assurance automobile et sélection adverse dans un modèle de Choquet

International 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

The value of information with neo-additive beliefs

When 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