Envy stable solutions for allocation problems with public resourses

Natalia I. Naumova

Contributions to game theory and management, Tome 12 (2019), pp. 261-272

Résumé

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.

Détail

Keywords: lexicographically maxmin solution, Wardrop equilibrium, envy stable solution, equal sacrifice solution.