Totally balanced combinatorial optimization games

Deng, Xiaotie; Ibaraki, Toshihide; Nagamochi, Hiroshi; Zang, Wenan

doi:10.1007/s101070050005

Cited by 55 publications

(58 citation statements)

References 17 publications

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“…Let it be A ∈ F ν (x, y). Let us define the following set, formed by the distances that appear in the characterization of the nucleolus, see (6), except for the grand coalition,…”

Section: Properties Of the Join-semilatticementioning

confidence: 99%

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Insights into the Nucleolus of the Assignment Game

2015

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Abstract:We show that the family of assignment matrices which give rise to the same nucleolus form a compact join-semilattice with one maximal element, which is always a valuation (see p.43, Topkis (1998)). We give an explicit form of this valuation matrix. The above family is in general not a convex set, but path-connected, and we construct minimal elements of this family. We also analyze the conditions to ensure that a given vector is the nucleolus of some assignment game.JEL Codes: C71.

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“…Let it be A ∈ F ν (x, y). Let us define the following set, formed by the distances that appear in the characterization of the nucleolus, see (6), except for the grand coalition,…”

Section: Properties Of the Join-semilatticementioning

confidence: 99%

“…We may choose different increasing linear paths from A to A 0 . 6 A path in X ⊆ M + m×m from A to B, A, B ∈ X , is a continuous function f from the unit interval I = [0, 1] to X , i.e. f : [0, 1] → X , with f (0) = A and f (1) = B.…”

Section: Properties Of the Join-semilatticementioning

confidence: 99%

Insights into the Nucleolus of the Assignment Game

2015

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“…Recently, Deng et al (1999Deng et al ( , 2000 have studied some families of combinatorial optimization games, namely packing and covering games, for which they prove total balancedness. Here, we have presented a different class exhibiting the same property.…”

Section: S (S)mentioning

confidence: 99%

“…The study of cooperative combinatorial optimization games, which are defined through characteristic functions given as optimal values of combinatorial optimization problems, is a fruitful topic (see, for instance, Shapley and Shubik, 1972;Dubey and Shapley, 1984;Granot, 1986;Tamir, 1992;Deng et al, 1999Deng et al, , 2000Faigle and Kern, 2000). There are characterizations of the total balancedness of several classes of these games.…”

Section: Introductionmentioning

confidence: 99%

Production-inventory games: A new class of totally balanced combinatorial optimization games

Guardiola

Meca

Puerto

2009

Games and Economic Behavior

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In this paper we introduce a new class of cooperative games that arise from production-inventory problems. Several agents have to cover their demand over a finite time horizon and shortages are allowed. Each agent has its own unit production, inventory-holding and backlogging cost. Cooperation among agents is given by sharing production processes and warehouse facilities: agents in a coalition produce with the cheapest production cost and store with the cheapest inventory cost. We prove that the resulting cooperative game is totally balanced and the Owen set reduces to a singleton: the Owen point. Based on this type of allocation we find a population monotonic allocation scheme for this class of games. Finally, we point out the relationship of the Owen point with other well-known allocation rules such as the nucleolus and the Shapley value.

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“…Okamoto (2003) showed that minimum vertex cover games are submodular if and only if the underlying graph is (K 3 , P 3 )-free, i.e., no induced subgraph is isomorphic to K 3 or P 3 , and that minimum coloring games are submodular if and only if the underlying graph is complete multipartite. Deng (2000) showed that minimum coloring games are totally balanced if and only if the underlying graph is perfect. Hamers et al (2011) showed that minimum coloring games have a Population Monotonic Allocation scheme if and only if the graph is (P 4 , 2K 2 )-free.…”

Section: Introductionmentioning

confidence: 99%