Years and Authors of Summarized Original Work
2001; Fang, Zhu, Cai, Deng
Problem Definition
The core is one of the most important solution concepts in cooperative game, which is based on the coalition rationality condition: no subgroup of the players will do better if they break away from the joint decision of all players to form their own coalition. The principle behind this condition can be seen as an extension to that of the Nash Equilibrium in noncooperative games. The work of Fang, Zhu, Cai, and Deng [4] discusses the computational complexity problems related to the cores of some cooperative game models arising from combinatorial optimization problems, such as flow games and Steiner tree games.
A cooperative game with side payments is given by the pair (N, v), where N = {1, 2, …, n} is the player set and v : 2N → R is the characteristic function. For each coalition S ⊆ N, the value v(S) is interpreted as the profit or cost achieved by the collective action of players in Swithout...
Recommended Reading
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Faigle U, Fekete S, Hochstättler W, Kern W (1997) On the complexity of testing membership in the core of min-cost spanning tree games. Int J Game Theory 26:361–366
Fang Q, Zhu S, Cai M, Deng X (2001) Membership for core of LP games and other games. In: COCOON 2001. Lecture notes in computer science, vol 2108. Springer, Berlin/Heidelberg, pp 247–246
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Fang, Q. (2015). Complexity of Core. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27848-8_80-2
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DOI: https://doi.org/10.1007/978-3-642-27848-8_80-2
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