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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-5217
    Keywords: cooperative game ; core
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In Driessen (1986) wurde für Spiele, die eine gewisse Bedingung erfüllen, gezeigt, da\ der Kern des Spieles in der konvexen Hülle von gewissen Vektoren der Marginalwerte liegt. Es wurde vermutet, da\ diese Inklusion ohne weitere Bedingung an das Spiel gilt. In dieser Note wird nun gezeigt, da\ die Inklusion für alle Spiele gilt.
    Notes: Abstract In Driessen (1986) it is shown that for games satisfying a certain condition the core of the game is included in the convex hull of the set of certain marginal worth vectors of the game, while it is conjectured that the inclusion holds without any condition on the game. In this note it is proved that the inclusion holds for all games.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-5217
    Keywords: cost allocation ; cooperative game ; one-machine scheduling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A combinatorial optimization problem can often be understood as the problem to minimize cost in a complex situation. If more than one party is involved, the solution of the optimization problem is not the end of the story. In addition it has to be decided how the minimal total cost has to be distributed among the parties involved. In this paper cost allocation problems will be considered arising from one-machine scheduling under additive and weakly increasing cost functions. The approach of the problem will be game theoretical and we shall in fact show that in many cases the games related to the cost allocation problems are balanced.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1432-5217
    Keywords: cooperative game ; balanced ; core ; tax ; bin packing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We investigate a cooperative game with two types of players envolved: Every player of the first type owns a unit size bin, and every player of the second type owns an item of size at most one. The value of a coalition of players is defined to be the maximum overall size of packed items over all packings of the items owned by the coalition into the bins owned by the coalition. We prove that forε=1/3 this cooperative bin packing game isε-balanced in the taxation model of Faigle and Kern (1993).
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1432-5217
    Keywords: cooperative game ; balanced core ; tax ; matching ; bin packing ; traveling salesman
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A model of taxation for cooperativen-person games is introduced where proper coalitions Are taxed proportionally to their value. Games with non-empty core under taxation at rateɛ-balanced. Sharp bounds onɛ in matching games (not necessarily bipartite) graphs are estabLished. Upper and lower bounds on the smallestɛ in bin packing games are derived and euclidean random TSP games are seen to be, with high probability,ɛ-balanced forɛ≈0.06.
    Type of Medium: Electronic Resource
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