# Strategic Online Facility Location

## Abstract

In this paper we consider a strategic variant of the online facility location problem. Given is a graph in which each node serves two roles: it is a strategic client stating requests as well as a potential location for a facility. In each time step one client states a request which induces private costs equal to the distance to the closest facility. Before serving, the clients may collectively decide to open new facilities, sharing the corresponding price. Instead of optimizing the global costs, each client acts selfishly. The prices of new facilities vary between nodes and also change over time, but are always bounded by some fixed value \(\alpha \). Both the requests as well as the facility prices are given by an online sequence and are not known in advance.

We characterize the optimal strategies of the clients and analyze their overall performance in comparison to a centralized offline solution. If all players optimize their own competitiveness, the global performance of the system is \(\mathcal {O}(\sqrt{\alpha }\cdot \alpha )\) times worse than the offline optimum. A restriction to a natural subclass of strategies improves this result to \(\mathcal {O}(\alpha )\). We also show that for fixed facility costs, we can find strategies such that this bound further improves to \(\mathcal {O}(\sqrt{\alpha })\).

## Keywords

Online algorithms Competitive analysis Facility location Algorithmic game theory## References

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