This article is cited in 4 papers

Claim Problems with Coalition Demands

Natalia I. Naumova

St. Petersburg State University, Faculty of Mathematics and Mechanics Universitetsky pr. 28, Petrodvorets, St. Petersburg, 198504, Russia

Abstract: 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.

Language: English