Geodesic
Computation problems for envy stable solutions of allocation problems with public resources
Contributions to game theory and management, Tome 14 (2021), pp. 302-311

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We consider generalizations of TU games with restricted cooperation in partition function form and propose their interpretation as allocation problems with several public resources. Either all resources are goods or all resources are bads. Each resource is distributed between points of its set and permissible coalitions are subsets of the union of these sets. Each permissible coalition estimates each allocation of resources by its gain/loss function, that depends only on the restriction of the allocation on that coalition. A solution concept of "fair" allocation (envy stable solution) was proposed by the author in (Naumova, 2019). This solution is a simplification of the generalized kernel of cooperative games and it generalizes the equal sacrifice solution for claim problems. An allocation belongs to this solution if there do not exist special objections at this allocation between permissible coalitions. For several classes of such problems we describe methods for computation selectors of envy stable solutions.
Keywords: Wardrop equilibrium, envy stable solution, games with restricted cooperation, equal sacrifice solution. 
@article{CGTM_2021_14_a22,
     author = {Natalia I. Naumova},
     title = {Computation problems for envy stable solutions of allocation problems with public resources},
     journal = {Contributions to game theory and management},
     pages = {302--311},
     publisher = {mathdoc},
     volume = {14},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2021_14_a22/}
}
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Natalia I. Naumova. Computation problems for envy stable solutions of allocation problems with public resources. Contributions to game theory and management, Tome 14 (2021), pp. 302-311. http://geodesic.mathdoc.fr/item/CGTM_2021_14_a22/