Geodesic
Claim Problems with Coalition Demands
Contributions to game theory and management, Tome 4 (2011), pp. 311-326.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a generalized claim problem, where each member of a fixed collection of coalitions of agents $\mathcal{A}$ has its claim. Several generalizations of the Proportional method and of the Uniform Losses method for claim problems are examined. For claim problems, the proportional solution, the proportional nucleolus, and the weighted entropy solution give the same results. For generalized claim problem conditions on $\mathcal{A}$ that provide the existence of the proportional solution and the existence of the weakly proportional solution are obtained. The condition on $\mathcal{A}$ for coincidence the weighted entropy solution and the weakly proportional solution is obtained. For such $\mathcal{A}$, we give an axiomatic justification for a selector of these solutions. For claim problems, the uniform losses solution, the nucleolus, and the least square solution give the same results, but for generalized claim problems conditions on $\mathcal{A}$ concerning existence results and inclusion results are similar to the case of proportional solution.
Keywords: claim problem, cooperative games, proportional solution, weighted entropy, nucleolus, constrained equal losses solution. 
@article{CGTM_2011_4_a22,
     author = {Natalia I. Naumova},
     title = {Claim {Problems} with {Coalition} {Demands}},
     journal = {Contributions to game theory and management},
     pages = {311--326},
     publisher = {mathdoc},
     volume = {4},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2011_4_a22/}
}
TY  - JOUR
AU  - Natalia I. Naumova
TI  - Claim Problems with Coalition Demands
JO  - Contributions to game theory and management
PY  - 2011
SP  - 311
EP  - 326
VL  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2011_4_a22/
LA  - en
ID  - CGTM_2011_4_a22
ER  - 
%0 Journal Article
%A Natalia I. Naumova
%T Claim Problems with Coalition Demands
%J Contributions to game theory and management
%D 2011
%P 311-326
%V 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2011_4_a22/
%G en
%F CGTM_2011_4_a22
Natalia I. Naumova. Claim Problems with Coalition Demands. Contributions to game theory and management, Tome 4 (2011), pp. 311-326. http://geodesic.mathdoc.fr/item/CGTM_2011_4_a22/

[1] Soviet Math. Dokl., 30:3 (1984), 583–587

[2] Bregman L. M., Naumova N. I., “Goal programming solutions generated by utility functions”, Lecture Notes in Economic and Math. Systems, 510, 2002, 495–514 | DOI | Zbl

[3] Bregman L. M., Romanovskij J. V., “Allotment and optimization in allocation problems”, Operations Research and Statistical Modeling, 3, ed. J. V. Romanovskij, Izdat. Leningrad. Univ., Leningrad, 1975, 137–162 (in Russian)

[4] Moulin H., “Axiomatic cost and surplus sharing”, Handbook of Social Choice and Welfare, Chapter 6, v. 1, eds. Arrow K. J., Sen A. K., Suzumura K., 2002, 289–357 | DOI

[5] Vestnik Leningrad. Univ. Math., 11 (1983), 67–73 | Zbl | Zbl

[6] Naumova N. I., “Associated consistency based on utility functions of coalitions”, Game Theory and Applications, 13, Nova Publishers, New York, 2008, 111–121

[7] Naumova N. I., “Generalized kernels and bargaining sets for families of coalitions”, The International Conference Game Theory and Management, Collected Papers (June 28–29 2007, St. Petersburg, Russia), Contributions to Game Theory and Management, 1, Graduate School of Management St. Petersburg State University, 2008, 346–360

[8] Peleg B., “Equilibrium points for open acyclic relations”, Canad. J. Math., 19 (1967), 366–369 | DOI | Zbl

[9] Thomson W., “Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey”, Mathematical Social Sciences, 45 (2003), 249–297 | DOI | Zbl