The effects of network topology on strategic behavior
The central question this thesis addresses is: if players are arranged in a network, and they are strategically interacting only with other players in their local neighborhood, how does the topology of the network affect the outcome of the interaction? We answer this question by combining techniques from computer science, economics, and sociology. ^ First, we introduce a graphical market model consisting of a bipartite network with buyers on one side and sellers on the other. Trade can only occur between a buyer and a seller if they are adjacent. We characterize when there will be variation in equilibrium wealth in terms of the network topology. Furthermore, we quantify the equilibrium wealth variation in social networks in terms of the degree distribution. Both of these results show that the network topology strongly affects the equilibrium behavior in this model. We also analyze a similar model where the players must buy the edges and trade according to the network that was purchased. We give a complete characterization of the equilibrium networks in this model. ^ Second, we assess a model of evolutionary game theory over networks. Evolutionary game theory has been used to model biological and social interactions where the dynamics are more imitative than optimizing. For two broad classes of graphs, we characterize which strategies could be played by a large fraction of the population that would guarantee they could not be overrun by any small mutant invasion. Here again, the topology of the networks under study had a direct impact on the structure of equilibria. ^ The final main component of this work is experimental in nature. A group of undergraduates was instructed to solve the graph coloring problem. Each one used our software system to control the color of one node in a network, and their objective was to arrive at a valid coloring. We varied the topology of the network by using different generative models from social network theory. One key finding of this experiment was that the group could color networks with low diameter much faster than networks with high diameter---showing that network topology impacted group behavior. ^
Economics, General|Computer Science
"The effects of network topology on strategic behavior"
(January 1, 2007).
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