Influencing Selfish Behavior in Congestion Games with Unknown Price-Sensitive Users

This paper focuses on the derivation of taxation mechanisms for improving system-level behavior in congestion games with unknown price-sensitive users. Here, a taxation mechanism represents a general rule for assigning local taxation functions to edges in a given network, e.g., Pigovian taxes or marginal-cost taxes. Recent results have identified taxation mechanisms that lead to optimal system-level behavior for the considered class of games; however, these mechanisms require that a system-designer has a complete characterization of network structure and the users’ sensitivities. Furthermore, the robustness of these mechanisms to mis-characterization in this information is unknown. With these issues in mind, this paper focuses on the derivation of robust taxation mechanisms – that is, taxation mechanisms that provide strong efficiency guarantees irrespective of the underlying network or user characteristics. With this goal in mind, we define a scaled marginal-cost taxation mechanism in which the edge taxation functions are derived without explicit knowledge of the network structure or the users’ sensitivities. We then derive the optimal scaled marginal-cost taxation mechanism that limits worst-case inefficiencies over these uncertainties for the class of parallel-network congestion games with affine latency functions. In other words, we derive the scaled marginal-cost taxation mechanism that optimizes the price of anarchy. Note that viewing the price of anarchy as a design objective represents a significant departure from most of the price of anarchy results in the existing literature.