Large Cores and Exactness

Biswas, Amit K.; Parthasarathy, T.; Potters, J.A.M.; Voorneveld, Mark

doi:10.1006/game.1998.0686

Cited by 49 publications

(35 citation statements)

References 6 publications

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“…Also, if a totally balanced game has a large core then it is exact (Sharkey 1982). The converse is false (Biswas et al 1999).…”

Section: Definitionmentioning

confidence: 99%

“…It is known (Biswas et al 1999) that there are exact classical games which are not extendable. Let (N , v) be such a game, and denote its core by C. Thus, for every coalition S ⊆ N , v(S) = min x∈C x(S).…”

Section: Theorem 7 Every Exact Game Is Extendable For Totally Balancmentioning

confidence: 99%

“…The following diagram summarizes the inclusion relations between these families when classical games are considered (see Biswas et al 1999;van Gellekom and Potters 1999). In what follows TB attached to an arrow means that the relation holds only for totally balanced games.…”

Section: Introductionmentioning

confidence: 99%

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On some families of cooperative fuzzy games

Azrieli

Lehrer

2007

Int J Game Theory

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In a fuzzy cooperative game the players may choose to partially participate in a coalition. A fuzzy coalition consists of a group of participating players along with their participation level. The characteristic function of a fuzzy game specifies the worth of each such coalition. This paper introduces well-known properties of classical cooperative games to the theory of fuzzy games, and studies their interrelations. It deals with convex games, exact games, games with a large core, extendable games and games with a stable core.

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“…Also, if a totally balanced game has a large core then it is exact (Sharkey 1982). The converse is false (Biswas et al 1999).…”

Section: Definitionmentioning

confidence: 99%

Section: Theorem 7 Every Exact Game Is Extendable For Totally Balancmentioning

confidence: 99%

See 1 more Smart Citation

On some families of cooperative fuzzy games

Azrieli

Lehrer

2007

Int J Game Theory

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show abstract

“…For a traditional cooperative game N, v , Biswas et al (1999) proved that the game is convex if and only if each subgame S, v , with S ⊂ N, is an exact game. In the sequel, we prove that a similar characterization holds true in the interval data setting.…”

Section: Theorem 1 Let W ∈ Ig N Then the Following Assertions Arementioning

confidence: 99%

“…, I n − I n ) ∈ C(|w|), with ∑ i∈S I i = w(S), ∑ i∈S I i = w(S) and ∑ i∈S (I i − I i ) = |w| (S). This can be used for extending the characterization of Biswas et al (1999) to interval games. Theorem 2.…”

Section: Proposition 6 Each Convex Interval Game W ∈ Ig N Is An Exacmentioning

confidence: 99%