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We consider the Stackelberg fuel pricing problem in which a company has to decide the fuel selling price at each of its gas stations in order to maximize its revenue, assuming that the selling prices of the competitors and the customers' preferences are known in advance. We show that, even in the basic case in which the road network is modeled by an undirected planar graph and the competitors discriminate on two different selling prices only, the problem is APX-hard. On the positive side, wedblp:conf/ictcs/VinciB14 fatcat:zekdgrcnbjgylni4id7q2wisom