Charles University, Faculty of Mathematicsand Physics
Prague, Czech Republic
16-19 July 2007


Jean-Yves Jaffray, Meglena Jeleva

Information Processing under Imprecise Risk with the Hurwicz criterion


An agent has Hurwicz criterion with pessimism-optimism index alpha under imprecise risk and adopts McClennen's Resolute Choice in sequential decision situations, i.e. evaluates strategies at the root of the decision tree by the Hurwicz criterion and enforces the best strategy, thus behaving in a dynamically consistent manner. We address two questions raised by this type of behavior: (i) is information processed correctly? and (ii) to what extent do unrealized outcomes influence decisions (non-consequentialism)? Partial answers are provided by studying: (i) the random sampling of a binary variable, and finding the influence of the pessimism-optimism index to be decreasing with the sample size, and the optimal decision rule to asymptotically only depend on the relative frequencies observed; and (ii) an insurance problem in which the agent chooses his coverage at period two after observing the period one outcome (accident or no accident); when no accident happened, a seemingly irrelevant data - the first period deductible level- is found to be able to influence the second period insurance choice. We analyse this result in relation with the existence and value of the pessimism-optimism degree.

Keywords. Imprecise risk, Hurwicz criterion, resolute choice, non-consequentialism, learning

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Authors addresses:

Jean-Yves Jaffray
LIP6 UPMC-Paris6
8,rue du Capitaine Scott
75015 Paris France

Meglena Jeleva
Meglena Jeleva
Maison des Sciences Economiques
U. Paris1
106, Bvd Hopital, 75012, Paris, France

E-mail addresses:

Jean-Yves Jaffray
Meglena Jeleva

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