Computation Problems for Envy Stable Solutions of Allocation Problems with Public Resources

Authors

DOI:

https://doi.org/10.21638/11701/spbu31.2021.22

Abstract

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

Downloads

Download data is not yet available.
 

References

Bregman, L. M. (1967) A relaxation method for determining a common point of convex sets, and its application to the solution of convex programming problems Zh. Vychisl. Mat. i Mat. Fiz., Vol.7, 620–631 (Russian), English translation in USSR Comput. Math. and Math. Phys., 7

Justman, M. (1977). Iterative processes with ”nucleolar” restrictons International Journal of Game Theory, 6, 189–212

Krylatov, A. Y. and Zakharov, V. V. (2017). Game-Theoretic Approach for Modeling of Selfish and Group Routing. In: Contributions to Game Theory and Management, 10, 162–174

Mazalov, V. V. (2010). Mathematical Game Theory and Applications. (Russian) Lan, Saint Petersburg, 448pp

Moulin, H. (2002) Axiomatic cost and surplus sharing Handbook on Social Choice and Welfare, 1 Ch.6, Arrow K.J., Sen A.K., Suzumura K. eds., 289–357

Naumova, N. (2011). Claim problems with coalition demands. Contributions to Game Theory and Management, 4, 311–326

Naumova, N. (2012). Generalized proportional solutions to games with restricted cooperation. Contributions to Game Theory and Management, 5, 230–242

Naumova, N. (2019). Envy stable solutions for allocation problems with public resources. Contributions to Game Theory and Managemen, 12, 261–272

Sudholter, P. and Peleg, B. (2007). Introduction to the Theory of Cooperative Games, 2nd edn. Springer, Berlin Heidelberg

Wardrop, J. G. (1952). Some theoretical aspects of road traffic research. Proc. Institution of Civil Engineers, 2, 325–378

Downloads

Published

2021-10-30

How to Cite

Naumova, N. I. (2021). Computation Problems for Envy Stable Solutions of Allocation Problems with Public Resources. Contributions to Game Theory and Management, 14, 302–311. https://doi.org/10.21638/11701/spbu31.2021.22

Issue

Vol. 14 (2021)

Section

Articles

License

Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.