Abstract
We consider routing games on grid network topologies. The social cost is the worst congestion in any of the network edges (bottleneck congestion). Each player’s objective is to find a path that minimizes the bottleneck congestion in its path. We show that the price of anarchy in bottleneck games in grids is proportional to the number of bends β that the paths are allowed to take in the grids’ space. We present games where the price of anarchy is \({\widetilde O}(\beta)\). We also give a respective lower bound of Ω(β) which shows that our upper bound is within only a poly-log factor from the best achievable price of anarchy. A significant impact of our analysis is that there exist bottleneck routing games with small number of bends which give a poly-log approximation to the optimal coordinated solution that may use an arbitrary number of bends. To our knowledge, this is the first tight analysis of bottleneck games on grids.
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© 2012 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
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Busch, C., Kannan, R., Samman, A. (2012). Bottleneck Routing Games on Grids. In: Jain, R., Kannan, R. (eds) Game Theory for Networks. GameNets 2011. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30373-9_21
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DOI: https://doi.org/10.1007/978-3-642-30373-9_21
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