We prove a general monotonicity result about Nash flows in directed networks, which generalizes earlier results and can be used for the design of
in the setting where each edge of the network is controlled by a different selfish agent, who incurs costs proportional to the usage of her edge. Moreover, we consider a mechanism design setting with
, which generalizes the well-known setting of one-parameter agents by allowing a fixed cost component as part of each agent’s private data. We give a complete characterization of the set of output functions that can be turned into truthful mechanisms for two-parameter agents. This characterization also motivates our choice of linear cost functions without fixed costs for the edges in the selfish routing setting.
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