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The composite equilibrium existence of the network and its algorithm

Author: ZhaoZuoJie
Tutor: GaoHongWei
School: Qingdao University
Course: Applied Mathematics
Keywords: mixed-flow network games heterogeneous profits heterogeneous link costs Nash networks
CLC: O157.5
Type: Master's thesis
Year: 2011
Downloads: 6
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Abstract


In this paper, we mainly do the research in the existence of Nash networks in mixed-flow models. We jump into the corresponding conclusion of the Nash networks in mixed-flow on the basis of the existence of Nash networks in one-way and two-way networks. In the mixed-flow networks, we construct a new B&G function and put it as basic payoff function of the players. According to the profits and costs of the payers in networks, we discuss different existence of Nash networks respectively.In chapter one, we introduce elementary knowledge and concepts of the network formation game in one-way and two-way networks and draw some mixed-networks’conclusions. We introduce definition of the link, arc, component, path in one-way and two-way networks, and draw corresponding conclusions in mixed-way networks on the basis of the new B&G function. At last, we give a example about the existence of the Nash equilibrium as well as the calculation example.In chapter two, we give two different methods of proof about the existence of Nash networks in one-way networks for different situation, as the starting point, we give existence theorem of the existence in mixed-flow networks.In chapter three, we give counter-examples about inexistence of Nash networks with homogeneous profits and heterogeneous link costs in mixed-flow networks, we show the Nash networks don’t always exist in the mixed-flow networks with homogeneous profits and heterogeneous link costs by giving examples about the inexinstence of Nash network, which has 5 nodes, at the same time, we prove that he Nash networks don’t always exist in the mixed-flow network with negative profits, which has 4 nodes.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Graph Theory
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