We study a geometric version of a simple non-cooperative network creation game introduced in [2], assuming Euclidean edge costs on the plane. The price of anarchy in such geometric games with k players is Θ(k). Hence, we consider the task of minimizing players incentives to deviate from a payment scheme, purchasing the minimum cost network. In contrast to general games, in small geometric games (2 players and 2 terminals per player), a Nash equilibrium purchasing the optimum network exists. This can be translated into a (1 + ε)-approximate Nash equilibrium purchasing the optimum network under more practical assumptions, for any ε > 0. For more players there are games with 2 terminals per player, such that any Nash equilibrium purchasing the optimum solution is at least (4/3 - ε)-approximate. On the algorithmic side, we show that playing small games with best-response strategies yields low-cost Nash equilibria. The distinguishing feature of our paper are new techniques to deal with the geometric setting, fundamentally different from the techniques used in [2]. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Hoefer, M., & Krysta, P. (2005). Geometric network design with selfish agents. In Lecture Notes in Computer Science (Vol. 3595, pp. 167–178). Springer Verlag. https://doi.org/10.1007/11533719_19
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