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We study pricing games in multi-hop relay networks where nodes price their services and route their traffic selfishly and strategically. Each node (1) makes a bid to each of its customers, specifying a charging function and a proposed traffic share, and (2) allocates its received traffic to its service providers. A node aims to maximize its profit from forwarding traffic. We show that the socially optimal routing can always be induced by an equilibrium where no node can increase its profit by unilaterally changing its bids. Inefficient equilibria arise in oligopolies due to the monopolistic pricing power of a superior relay. It results in finite price of anarchy if marginal cost functions are concave, but unbounded price of anarchy when they are convex. Pricing games of general topology suffer from the intrinsic multi-hop network structure, which gives rise to infinite price of anarchy.

Pricing, Competition, and Routing for Selfish and Strategic Nodes in Multi-Hop Relay Networks