An additive subfamily of enlargements of a maximally monotone operator

We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the family of enlargements introduced by Svaiter. When the operator under consideration is the subdifferential of a convex lower semicontinuous proper function, we prove that some members of the subfamily are smaller than the classical $\epsilon$-subdifferential enlargement widely used in convex analysis. We also recover the epsilon-subdifferential within the subfamily. Since they are all additive, the enlargements in our subfamily can be seen as structurally closer to the $\epsilon$-subdifferential enlargement

On Demand Responsiveness in Additive Cost Sharing

We propose two new axioms of demand responsiveness for additive cost sharing with variable demands. Group Monotonicity requires that if a group of agents increase their demands, not all of them pay less. Solidarity says that if agent i demands more, j should not pay more if k pays less. Both axioms are compatible in the partial responsibility theory postulating Strong Ranking, i.e., the ranking of cost shares should never contradict that of demands. The combination of Strong Ranking , Solidarity and Monotonicity characterizes the quasi-proportional methods, under which cost shares are proportional to 'rescaled' demands. The alternative full responsibility theory is based on Separability, ruling out cross-subsidization when costs are additively separable. Neither the Aumann-Shapley nor the Shapley-Shubik method is group monotonic. On the otherhand, convex combinations of "nearby" fixed-path methods are group-monotonic: the subsidy-free serial method is the main example. No separable method meets Solidarity, yet restricting the axiom to submodular (or supermodular) cost functions leads to a characterization of the fixed-flow methods, containing the Shapley-Shubik and serial methods.

Common Mathematical Foundations of Expected Utility and Dual Utility Theories

We show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas: the separation principle of convex analysis, and integral representations of continuous linear functionals from functional analysis. Our analysis reveals the dual character of utility functions. We also derive new integral representations of dual utility models

Parametric Weighting Functions

This paper provides behavioral foundations for parametric weighting functions under rankdependent utility. This is achieved by decomposing the independence axiom of expected utility into separate meaningful properties. These conditions allow us to characterize rank-dependent utility with power and exponential weighting functions. Moreover, by restricting the conditions to subsets of the probability interval, foundations of rank-dependent utility with parametric inverse-S shaped weighting functions are obtained. --Comonotonic independence,probability weighting function,preference foundation,rank-dependent utility

On the decomposition of Generalized Additive Independence models

The GAI (Generalized Additive Independence) model proposed by Fishburn is a generalization of the additive utility model, which need not satisfy mutual preferential independence. Its great generality makes however its application and study difficult. We consider a significant subclass of GAI models, namely the discrete 2-additive GAI models, and provide for this class a decomposition into nonnegative monotone terms. This decomposition allows a reduction from exponential to quadratic complexity in any optimization problem involving discrete 2-additive models, making them usable in practice