The Price of Anarchy Under Nonlinear and Asymmetric Costs

Abstract

In this paper we characterize the "price of anarchy", i.e., the inefficiency between user and system optimal solutions, when costs are non-separable, asymmetric and nonlinear, generalizing earlier work that has addressed "price of anarchy" under separable costs. The generalization models traffice equilibria, competitive multi-period pricing and competitive supply chains. The bounds established in the paper are tight and explicitly account for the degeee of asymmetry and nonlinearity of the cost function. We introduce and alternate proof method for providing bounds that uses ideas from semidenfinite optimization. Finally, in the context of nulti-period pricing our analysis establishes that user and system optimal soulutions coincide.