Envy stable solutions for allocation problems with public resourses
Natalia I. Naumova St. Petersburg State University, Faculty of Mathematics and Mechanics, Universitetsky pr. 28, St. Petersburg, 198504, Russia
Аннотация:
We consider problems of "fair" distribution of several different public resourses. If
$\tau$ is a partition
of a finite set
$N$, each resourse
$c_j$ is distributed between points of
$B_j\in \tau$.
We suppose that either all resourses are goods or all resourses are bads.
There are finite projects, each project use points from its subset of
$N$ (its coalition).
$\mathcal{A}$ is the set of such coalitions.
The gain/loss function of a project at an allocation depends only on the restriction of the
allocation on the coalition of the project.
The following 4 solutions are considered:
the lexicographically
maxmin solution, the lexicographically
minmax solution, a generalization of Wardrop solution.
For fixed collection of gain/loss functions, we define envy stable allocations with respect to
$\Gamma$, where
the projects compare their gains/losses at fixed allocation if their coalitions are
adjacent in
$\Gamma$. We describe conditions on
$\mathcal{A}$,
$\tau$, and
$\Gamma$ that ensure
the existence of envy stable solutions, and conditions that ensure the enclusion of the first three solutions
in envy stable solution.
Ключевые слова:
lexicographically maxmin solution, Wardrop equilibrium, envy stable solution, equal sacrifice solution.
Язык публикации: английский