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Some Algorithic Results on Solutions of Flow Games

Author: ZuoLinCheng
Tutor: FangQiZhi
School: Ocean University of China
Course: Operational Research and Cybernetics
Keywords: Cooperative games Network flow Linear Programming Dual Core Relative N- nuclear
CLC: O225
Type: Master's thesis
Year: 2011
Downloads: 18
Quote: 0
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Abstract


Cooperative game considered the central issue is how to be fair and reasonable allocation of the Union 's overall cost (gain) to each member of the Alliance N . Depending on the reasonable requirements of different countermeasures solution concept , such as core , N- nuclear , stable sets and Shapley value . SOLUTIONS WITH definition is often very complex , algorithm design is an important issue in the combination of cooperative games . The network flow countermeasures from the maximum flow of income distribution in the network is an important class combination of cooperative games , the algorithm is of great significance . This paper mainly discusses the core of the network flow countermeasures and relative N- core algorithms , the main results are : ( 1 ) to discuss the core elements of a simple model of network flow countermeasures with public arc portrayed ; maximum flow problem arc - flow expression type and linear programming duality theory gives a new proof of the necessary and sufficient conditions for core non- empty ; proved on the basis of the response of the core of several algorithmic problems ( judgment of non- core empty decide for a given allocation whether vested in the core, the to construct core elements ) are solvable in polynomial time . (2 ) For the simple network flow countermeasures model does not have a public arc , the establishment of effective characterization of the relative N- nuclear ; first prove the maximum flow value is equal to 1 , the same relative N- nuclear countermeasures core network , is not necessarily a single set of points ; Second Kopelowitz's sequence of linear programming method and linear programming duality theory prove when the value is greater than the maximum flow in the network relative N- nuclear and N- 1 nuclear is the same ( with a single point set ) , and the relative N- endorsed solving polynomial time in the number of the players .

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CLC: > Mathematical sciences and chemical > Mathematics > Operations Research > Game theory ( game theory )
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