Envy Stable Solutions for Allocation Problems with Public Resourses

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Abstract

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 is an element of 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). 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 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.

Original languageEnglish
Title of host publicationCONTRIBUTIONS TO GAME THEORY AND MANAGEMENT, VOL XII
EditorsLA Petrosyan, NA Zenkevich
PublisherИздательство Санкт-Петербургского университета
Pages261-272
Number of pages12
ISBN (Print)*****************
StatePublished - 2019
Event12th International Conference on Game Theory and Management, GMT2018 - St Petersburg, Russian Federation
Duration: 27 Jun 201829 Jun 2018

Publication series

NameContributions to Game Theory and Management
PublisherST PETERSBURG UNIV GRAD SCH MANAGEMENT
Volume12
ISSN (Print)2310-2608

Conference

Conference12th International Conference on Game Theory and Management, GMT2018
CountryRussian Federation
CitySt Petersburg
Period27/06/1829/06/18

Keywords

  • lexicographically maxmin solution
  • Wardrop equilibrium
  • envy stable solution
  • equal sacrifice solution

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