Farhad Hüsseinov

Existence of efficient envy-free allocations of a heterogeneous divisible commodity with nonadditive utilities

This paper studies the existence of Pareto optimal, envy-free allocations of a heterogeneous, divisible commodity for a finite number of individuals. We model the commodity as a measurable space and make no convexity assumptions on the preferences of individuals. We show that if the utility function of each individual is uniformly continuous and strictly monotonic with respect to set inclusion, and if the partition matrix range of the utility functions is closed, a Pareto optimal envy-free partition exists. This result follows from the existence of Pareto optimal envy-free allocations in an extended version of the original allocation problem.

Concave measures and the fuzzy core of exchange economies with heterogeneous divisible commodities

The main purpose of this paper is to prove the existence of the fuzzy core of an exchange economy with a heterogeneous divisible commodity in which preferences of individuals are given by nonadditive utility functions defined on a @s-algebra of admissible pieces of the total endowment of the commodity. The problem is formulated as the partitioning of a measurable space among finitely many individuals. Applying the Yosida-Hewitt decomposition theorem, we also demonstrate that partitions in the fuzzy core are supportable by prices in L^1.

Existence of the core in a heterogeneous divisible commodity exchange economy

We consider the exchange of a heterogeneous divisible commodity modeled as a measurable space. Under rational, continuous and convex preferences over characteristic measures a weak core is shown to exist. Further, a core exists if characteristic measures are mutually absolutely continuous. Applied to the land trading economy, the core existence results in Berliant (J Math Econ 14:53–56, 1985) and Dunz (Reg Sci Urban Econ 21:73–88, 1991) are obtained.

Concave Measures and the Fuzzy Core of Exchange Economies with Heterogeneous Divisible Commodities

The main purpose of this paper is to prove the existence of the fuzzy core of an exchange economy with a heterogeneous divisible commodity in which preferences of individuals are given by nonadditive utility functions defined on a -algebra of admissible pieces of the total endowment of the commodity. The problem is formulated as the partitioning of a measurable space among finitely many individuals. Applying the Yosida–Hewitt decomposition theorem, we also demonstrate that partitions in the fuzzy core are supportable by prices in L1.

[alpha]-maxmin solutions to fair division problems and the structure of the set of Pareto utility profiles

A simple proof of the equivalence of Pareto optimality plus positiveness and [alpha]-maxmin optimality, dispensing with the assumption of closedness of the utility possibility set, is given. Also the structure of the set of Pareto optimal utility profiles is studied.

Relaxation of multidimensional variational problems with constraints of general form

This paper is devoted to further developement of an idea of a well-known theorem of Bogolubov [2]. Here we construct a relaxation of multidimensional variational problems with constraints of rather general form on gradients of admissible functions; it is assumed that the gradient of an admissible function belongs to an arbitrary bounded set. This relaxation involves as a class of admissible functions the closure of the class of admissible functions of the original problem in the topology of uniform convergence, and uses a theorem characterizing this closure, which is proved in [15]. The case when the gradient of an admissible function is constrained within a bounded closed convex body is studied in the works [13,15,19]. The study of multidimensional variational problems was started in 1970s by Ekeland and Temam [13]. The existing literature on relaxation of variational problems, including two monographs by Buttazzo [3] and Dacorogna [9], and the review paper by Marcellini [18] containing a considerable list of references, is quite rich. However, the author failed to And a setting similar to that of the paper. For the most recent results on relaxation and related topics see [1,4–8,11,14]. This paper deals with the case where an integrand depends on a scalar function of several variables. At the end of the paper we will make a conjecture on generalization of the main relaxation result of the paper to the case of an integrand depending on a vector function of several variables. We also make a conjecture on generalization of

Characterization of spannability of functions

Abstract Possibility of representation of a value of convexification of function at the given point as a convex combination of the values of function (spannability) is studied. Spannability of functions turned out to be important in different fields e.g. in the study of quasi-cores of monetary economies with nonconvex preferences (mathematical economics), in the theory of relaxation of variation problems (variational calculus). Apparently, Shapley and Shubik ( Econometrica , 1966, 34, 805–827) were first to discuss it.