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dc.contributor.authorSteiner, David 18:52:34 (GMT) 18:52:34 (GMT)
dc.description.abstractBargaining theory seeks to answer the question of how to divide a jointly generated surplus between multiple agents. John Nash proposed the Nash Bargaining Solution to answer this question for the special case of two agents. Kleinberg and Tardos extended this idea to network games, and introduced a model they call the Bargaining Game. They search for surplus divisions with a notion of fairness, defined as balanced solutions, that follow the Nash Bargaining Solution for all contracting agents. Unfortunately, many networks exist where no balanced solution can be found, which we call unstable. In this thesis, we explore methods of changing unstable network structures to find fair bargaining solutions. We define the concept of Blocking Sets, introduced by Biro, Kern and Paulusma, and use them to create stability. We show that by removing a blocking set from an unstable network, we can find a balanced bargaining division in polynomial time. This motivates the search for minimal blocking sets. Unfortunately this problem is NP-hard, and hence no known efficient algorithm exists for solving it. To overcome this hardness, we consider the problem when restricted to special graph classes. We introduce a O(1)-factor approximation algorithm for the problem on planar graphs with unit edge weights. We then provide an algorithm to solve the problem optimally in graphs of bounded treewidth, which generalize trees.en
dc.publisherUniversity of Waterlooen
dc.subjectNetwork Bargainingen
dc.subjectBlocking Setsen
dc.titleNetwork Bargaining: Creating Stability Using Blocking Setsen
dc.typeMaster Thesisen
dc.subject.programComputer Scienceen of Computer Scienceen
uws-etd.degreeMaster of Mathematicsen

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