Houston, TX 77005
4:00 p.m. Monday, April 8, 2013
On Campus | Alumni
In the first paper, we consider the problem of fairly dividing l divisible goods among n agents with the generalized Leontief preferences. We propose and characterize the class of generalized egalitarian rules which satisfy efficiency, group strategy-proofness, anonymity, resource monotonicity, population-monotonicity, envy-freeness and consistency. On the Leontief domain, our rules generalize the egalitarian-equivalent rules with reference bundles. We also extend our rules to agent-specific and endowment-specific egalitarian rules. The former is a larger class of rules satisfying all the previous properties except anonymity and envy-freeness. The latter is a class of efficient, group strategy-proof, anonymous and individually rational rules when the resources are assumed to be privately owned. The second paper axiomatizes a class of preferences displaying decreasing absolute uncertainty aversion, which allows a decision maker to be more willing to take uncertainty-bearing behavior when he becomes wealthier. In our first main result, we obtain three equivalent representations. The first is a variation on the constraint criterion of Hansen and Sargent (2001). The other two generalize Gilboa and Schmeidler (1989)’s maxmin criterion and Maccheroni, Marinacci and Rustichini (2006)’s variational representation. This class, when restricted to preferences exhibiting constant absolute uncertainty aversion, is exactly Maccheroni, Marinacci and Rustichini (2006)’s variational preferences. In our second main result, we establish relationships among the representations for several important classes within variational preferences. The last paper develops a model of uncertainty in which a decision maker evaluates an act based on his aspiration and his confidence in this aspiration. Each act corresponds to a trade-off line between the two criteria: The more he aspires, the less his confidence in achieving the aspiration level. The decision maker ranks an act by the optimal combination of aspiration and confidence on its trade-off line according to an aggregating preference of his over the two-criteria plane. To reveal the decision maker's perception about uncertainty, this paper introduces confidence orders in addition to preference orders; the confidence orders compare the decision maker's confidence in all aspiration levels of all acts. Axioms are imposed on both confidence and preference orders, which yields a capacity over all priors to represent the confidence order, and the above decision rule to represent the preference order. The aggregating preference over the aspiration and confidence criteria plane is endogenously determined.