Improved Bounds for Facility Location Games with Fair Cost Allocation

We study Facility Location games played by n agents situated on the nodes of a graph. Each agent orders installation of a facility at a node of the graph and pays connection cost to the chosen node, and shares fairly facility installation cost with other agents having chosen the same location. This game has pure strategy Nash equilibria, that can be found by simple improvements performed by the agents iteratively. We show that this algorithm may need super-polynomial Ω(2 1 2 ) steps to converge. For metric graphs we show that approximate pure equilibria can be found in polynomial time. On metric graphs we consider additionally strong equilibria; previous work had shown that they do not always exist. We upper bound the overall (social) cost of α-approximate strong equilibria within a factor O(α lnα) of the optimum, for every α ≥ 1.