About A Model For Network Creation Game

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Saghafian, Morteza | 2011

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 43130 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Jafari, Amir
Abstract:
We consider a network creation game in which, each player(vertex) has bounded budget to draw edges to other vertices. Each player wants to minimize its local diameter in MAX version, and its sum of distances to other vertices in SUM version.
In this thesis, we first prove that the problem of finding the best response for each player in this network creation game, is NP-Hard. But we show that always there exists a Pure Nash Equilibria for each of the versions. Then we focus on the diameter of equilibrium graphs. In Unit Budget case (when each player’s budget is one) we show that the diameter of each equilibrium graph in O(1), and always there exists a Mixed Nash Equilibirum. For each n, we construct an example of equilibrium tree with diameter [(2n+2)/3] in MAX version, and θ(logn) in SUM version. We prove that this bounds are tight for equilibrium trees
Keywords:
Game Theory ; Bounded Budget ; Nash Equilibrium Point ; Network Creation ; Graph Diameter