Composition of games without side payments

Vilkov, V. B.

doi:10.1007/bf01069125

Cited by 13 publications

(10 citation statements)

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“…Second, they assume that for all S ⊂ N , the value of V (S) is downward-sloping 4 : for all x, y ∈ V (S) such that x S = y S and that x S ≤ y S , there exists z ∈ V (S) such that x S z S , which is a weaker version of the boundary condition introduced by Vilkov (1977). As was discussed in Greenberg (1985), such boundary conditions are not plausible for NTU theory because "corner games" do not satisfy this condition.…”

Section: Example 4 (Four-person Game)mentioning

confidence: 99%

“…The convexity of games with nontransferable utility (NTU games) was first defined by Vilkov (1977) as an extension of the convexity of games with transferable utility (TU games), called ordinal convexity. While ordinal convex games arise in various economic applications 1 , they do not inherit interesting properties from the TU convex games.…”

Section: Introductionmentioning

confidence: 99%

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Strong convexity of NTU games

Masuzawa

2012

Int J Game Theory

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Section: Example 4 (Four-person Game)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Strong convexity of NTU games

Masuzawa

2012

Int J Game Theory

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“…It follows from his study that a convex VC is stable. His proof relies on a result on cores of ordinal games (see Vilkov 1977, or more directly Greenberg 1985. The nice result however is restricted to maximal VCs: A maximal VC is stable if and only if it is convex or put in another way, if and only if it is both superadditive and subadditive.…”

Section: Introductionmentioning

confidence: 99%

Neutral veto correspondences with a continuum of alternatives

Abdou

1988

Int J Game Theory

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A veto theory is constructed for a finite committee and a measure space of alternatives.Strategical and descriptive concepts of veto and effectivity functions are extended to the model. We show that under some natural assumptions a neutral veto correspondence can be represented by a real veto power function. As in the discrete case we prove that a stable VC is well-behaved from above and from below, that a convex VC is stable, and that a maximal VC is stable if and only if it is superadditive and subadditive.

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“…It turns out that this type of NTU-bankruptcy games does satisfy ordinal convexity (cf. Vilkov, 1977) together with coalitional merge convexity (cf. Hendrickx, Borm and Timmer, 2002).…”

Section: Introductionmentioning

confidence: 99%

Nontransferable Utility Bankruptcy Games

2014

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. (0)10 408 9031 Duisenberg school of finance is a collaboration of the Dutch financial sector and universities, with the ambition to support innovative research and offer top quality academic education in core areas of finance. In this paper, we analyze bankruptcy problems with nontransferable utility (NTU) from a game theoretical perspective by redefining corresponding NTU-bankruptcy games in a tailor-made way. It is shown that NTU-bankruptcy games are both coalitional merge convex and ordinal convex. Generalizing the notions of core cover and compromise stability for transferable utility (TU) games to NTU-games, we also show that each NTU-bankruptcy game is compromise stable. Thus, NTU-bankruptcy games are shown to retain the two characterizing properties of TU-bankruptcy games: convexity and compromise stability. As a first example of a game theoretical NTU-bankruptcy rule, we analyze the NTU-adjusted proportional rule and show that this rule corresponds to the compromise value of NTU-bankruptcy games. Terms of use: Documents in

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Composition of games without side payments

Cited by 13 publications

References 1 publication

Strong convexity of NTU games

Strong convexity of NTU games

Neutral veto correspondences with a continuum of alternatives

Nontransferable Utility Bankruptcy Games

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