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Two Cooperative and Non-Cooperative Game Models with Graph Structures

Author: LiLei
Tutor: LiXueLiang
School: Nankai University
Course: Applied Mathematics
Keywords: TU game covering value eiffciency Harsanyi dividend acyclic di?graph game dynamic Nash action theory
CLC: O157.5
Type: PhD thesis
Year: 2012
Downloads: 159
Quote: 0
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Abstract


Game theory studys how the players act and how the fruits of their work areallocated. On the basis of whether cooperation is permitted among the players,games can be classified as cooperative and non-cooperative types. We study thegames with graph structures in cooperative and non-cooperative ways.We introduce a novel covering method to compute values for acyclic digraphgames, and we call the values obtained by this method the covering values. Thesevalues may be considered as natural extensions of the component eiffcient solu?tions for line-graph games studied by van den Brink et al.(Econ Theory33:349-364,2007), and the tree values studied by Khmelnitskaya (Theory Decis69(4):657-669,2010). With the new method, we reinterpret the tree values pro?posed by Khmelnitskaya in2010. Besides, we propose the covering values in thedigraph game with general acyclic digraph structures presenting lfow situationswhen some links may merge while others split into several separate ones. We giveaxiomatizations of these values, and interpret these values in terms of dividenddistributions.People are closely connected in learning, working and everyday life. Citiesare linked by more than one paths. When the connectivity of a graph increases,the structure of the graph becomes more stable. In our work, we modify the payofffunctions of BG-models proposed by Bala and Goyal (Econometria68(5):1181-1230,2000), such that agents benefit only when they are two way2-connected.We study the Nash, eiffcient and dynamic properties of two way2-connectedmodel, and compare it with BG-model. We ifnd that, most of the time, theempty graph, the cycle, and the centered graph are Nash networks. And the social implications of the empty graph and centered graph are discussed. Theoccurrence of an empty network is usually unexpected in a dynamic process, it cannot be stopped from happening by increasing the density of the initial network.The centered graph is kind of similar with the star structure in BG-model.

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