A novel concept of equilibrium over a network

Abstract

We define and analyze a novel concept of equilibrium over a network, which we refer to as location equilibrium. Its applications include area coverage for taxi drivers, human migration and task assignment for a server network. In particular, we show that a specific instance of the location equilibrium problem is equivalent to the Wardrop equilibrium problem on a specific network. Further, we show that finding a location equilibrium is equivalent to solving a variational inequality with an operator which is in general not monotone. Based on the relation to the Wardrop equilibrium, we propose the use of the extragradient algorithm and show its convergence to a specific location equilibrium. The findings are applied to a numerical study of area coverage for taxi drivers in Hong Kong.