A Characterization of the Nucleolus for Convex Games

Arin, Javier; Iñarra, Elena

doi:10.1006/game.1997.0601

Cited by 14 publications

(10 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, S m } ∈ B be a balanced collection of coalitions. The next lemma follows from Arin and Inarra (1998, Theorem 3.2) Lemma 2.2 (Arin and Inarra 1998) …”

Section: E(s X) = V(s) − X(s)mentioning

confidence: 90%

A polynomial time algorithm for computing the nucleolus for a class of disjunctive games with a permission structure

2010

View full text Add to dashboard Cite

Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many such allocation problems there is some hierarchical ordering of the players. In this paper we consider a class of games with a permission structure describing situations in which players in a cooperative TU-game are hierarchically ordered in the sense that there are players that need permission from other players before they are allowed to cooperate. The corresponding restricted game takes account of the limited cooperation possibilities by assigning to every coalition the worth of its largest feasible subset. In this paper we provide a polynomial time algorithm for computing the nucleolus of the restricted games corresponding to a class of games with a permission structure which economic applications include auction games, dual airport games, dual polluted river games and information market games.

show abstract

“…, S m } ∈ B be a balanced collection of coalitions. The next lemma follows from Arin and Inarra (1998, Theorem 3.2) Lemma 2.2 (Arin and Inarra 1998) …”

Section: E(s X) = V(s) − X(s)mentioning

confidence: 90%

A polynomial time algorithm for computing the nucleolus for a class of disjunctive games with a permission structure

2010

View full text Add to dashboard Cite

show abstract

“…Arin and Inarra (1998) prove that, given a convex game, the collection of coalitions with minimal satisfaction with respect to the prenucleolus of the game contains either a partition or an antipartition. In the case of the SD-prenucleolus of SD-relevant games only antipartitions should be considered, as the following lemma shows.…”

Section: Lemma 12 Let (N V) Be a Tu Game And X ∈ X (N V) Let C Bmentioning

confidence: 99%

A monotonic core solution for convex TU games

Arin

Katsev

2015

Int J Game Theory

View full text Add to dashboard Cite

show abstract

“…Moreover, we also show another interesting property which is the fact that the nucleolus (and so the kernel) of a zero-monotonic almost-convex game coincides with the nucleolus (the kernel) of a suitable convex game associated. This property allows for the application of specific efficient algorithms to calculate the nucleolus of zero-monotonic almost-convex game (see Faigle et al,2001;Arin and Iñarra, 1998;Kuipers, 1996).…”

Section: It Is Straightforward Thatmentioning

confidence: 99%

The bargaining set for almost-convex games

et al. 2012

View full text Add to dashboard Cite

We extend well-known results for convex games (Maschler et al., 1972) to a more general class of games named almost-convex games, that is, games where all proper subgames are convex. We prove that for any balanced almost-convex game the bargaining set coincides with the core. We also prove that the kernel of any zero-monotonic almost-convex game reduces to the nucleolus. In contrast to the above results, the core of a balanced almostconvex game is stable in the sense of von Neumann-Morgenstern if and only if the game is convex.

show abstract

A Characterization of the Nucleolus for Convex Games

Cited by 14 publications

References 13 publications

A polynomial time algorithm for computing the nucleolus for a class of disjunctive games with a permission structure

A polynomial time algorithm for computing the nucleolus for a class of disjunctive games with a permission structure

A monotonic core solution for convex TU games

The bargaining set for almost-convex games

Contact Info

Product

Resources

About