Abstract
We consider a new facility game, namely, an obnoxious facility game where the facility is undesirable and all agents try to be as far away from the facility as possible. The social cost is the total distance between the agents and the facility. However, an obnoxious facility is placed based on the reported locations of the selfish agents. We are interested in a mechanism to decide the facility location so that the social cost is maximized. In this paper, we give a first attempt for this game on a path. Our main results include a 3-approximation group strategy-proof deterministic mechanism, which is best possible if the facility can only take one of the endpoints on the path, and two group strategy-proof randomized mechanisms with approximation ratio of \(\frac{5}{3}\) and \(\frac{3}{2}\), respectively.
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Cheng, Y., Yu, W., Zhang, G. (2011). Mechanisms for Obnoxious Facility Game on a Path. In: Wang, W., Zhu, X., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2011. Lecture Notes in Computer Science, vol 6831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22616-8_21
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DOI: https://doi.org/10.1007/978-3-642-22616-8_21
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