Optimal mechanisms for robust coordination in congestion games

Uninfluenced social systems often exhibit suboptimal performance; a common mitigation technique is to charge agents specially-designed taxes, influencing the agents´ choices and thereby bringing aggregate social behavior closer to optimal. In general, the efficiency guaranteed by a particular taxation methodology is limited by the quality of information available to the tax-designer. If the tax-designer possesses a perfect characterization of the system, it is often straightforward to design taxes which perfectly optimize the behavior of the agent population. In this paper, we investigate situations in which the tax-designer lacks such a perfect characterization and must design taxes that are robust to a variety of model imperfections. Specifically, we study the application of taxes to a network-routing game, and we assume that the tax-designer knows neither the network topology nor the tax-sensitivities and demands of the agents. Nonetheless, we show that it is possible to design taxes that guarantee that network flows are arbitrarily close to optimal flows, despite the fact that agents´ tax-sensitivities are unknown to us. We term these taxes “universal,” since they enforce optimal behavior in any routing game without a priori knowledge of the specific game parameters. In general, these taxes may be very high; accordingly, for affine-cost parallel-network routing games, we explicitly derive the optimal bounded tolls and the best-possible efficiency guarantee as a function of a toll upper-bound.