Even and odd marginal worth vectors, Owen's multilinear extension and convex games

Rafels, Carles; Ybern, Neus

doi:10.1007/bf01240037

Cited by 6 publications

(3 citation statements)

References 10 publications

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“…This result is analogous to that of Rafels and Ybern (1995) for convex games. In fact, we can use Lemma 3.1 to find smaller sets that imply compromise stability whenever all the larginals of the set are in the core.…”

Section: The Neighbor Argumentsupporting

confidence: 61%

Characterizing Compromise Stability of Games Using Larginal Vectors

2011

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The core cover of a TU-game is a superset of the core and equals the convex hull of its larginal vectors. A larginal vector corresponds to an order of the players and describes the efficient payoff vector giving the first players in the order their utopia demand as long as it is still possible to assign the remaining players at least their minimum right. A game is called compromise stable if the core is equal to the core cover, i.e. the core is the convex hull of the larginal vectors. In this paper we describe two ways of characterizing sets of larginal vectors that satisfy the condition that if every larginal vector of the set is a core element, then the game is compromise stable. The first characterization of these sets is based on a neighbor argument on orders of the players. The second one uses combinatorial and matching arguments and leads to a complete characterization of these sets. We find characterizing sets of minimum cardinality, a closed formula for the minimum number of orders in these sets, and a partition of the set of all orders in which each element of the partition is a minimum characterizing set.

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Section: The Neighbor Argumentsupporting

confidence: 61%

Characterizing Compromise Stability of Games Using Larginal Vectors

2011

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“…Shapley (1971) and Ichiishi (1981) showed that a game is convex if and only if all marginal vectors are core elements. In Rafels, Ybern (1995) it is shown that if all even marginal vectors are core elements, then all odd marginal vectors are core elements as well, and vice versa. Hence, if all even or all odd marginal vectors are core elements, then the game is convex.…”

Section: Introductionmentioning

confidence: 99%

Characterizing convexity of games using marginal vectors

Velzen

Hamers

Norde

2004

Discrete Applied Mathematics

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“…A set of marginal vectors characterizes convexity if it satisfies the condition that a game is convex whenever all marginal vectors of this set are core elements. Rafels and Ybern (1995) showed that the set consisting of either all even or all odd marginal vectors are sets that characterize convexity. Van Velzen et al (2002) improved this result by finding such characterizing sets with a smaller cardinality by using a neighbor argument showing that if two consecutive neighbors of a marginal vector are in the core, so is the marginal vector itself.…”

Section: Introductionmentioning

confidence: 99%

C-complete sets for compromise stable games

2014

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The core cover of a TU-game is a superset of the core and equals the convex hull of its larginal vectors. A larginal vector corresponds to an ordering of the players and describes the efficient payoff vector giving the first players in the ordering their utopia demand as long as it is still possible to assign the remaining players at least their minimum right. A game is called compromise stable if the core is equal to the core cover, i.e. the core is the convex hull of the larginal vectors. This paper analyzes the structure of orderings corresponding to larginal vectors of the core cover and conditions ensuring equality between core cover and core. We introduce compromise complete (or c-complete) sets that satisfy the condition that if every larginal vector corresponding to an ordering of the set is a core element, then the game is compromise stable. We use combinatorial arguments to give a complete characterization of these sets. More specifically, we find c-complete sets of minimum cardinality and a closed formula for the minimum number of orderings in c-complete sets.

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Even and odd marginal worth vectors, Owen's multilinear extension and convex games

Cited by 6 publications

References 10 publications

Characterizing Compromise Stability of Games Using Larginal Vectors

Characterizing Compromise Stability of Games Using Larginal Vectors

Characterizing convexity of games using marginal vectors

C-complete sets for compromise stable games

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