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# Distributed dynamics to achieve a location equilibrium.

This talk focuses on a new concept of equilibrium over a network, referred to as location equilibrium. Its applications include area coverage for taxi drivers, human migration and task assignment for a server network. The proposed equilibrium is connected to two related concepts, namely the Wardrop equilibrium in transportation and the migration equilibrium.

Finding a location equilibrium is equivalent to solving a variational inequality which in general is not monotone. The main focus of the talk is on algorithmic convergence: first it is shown that a well-known algorithm achieves a location equilibrium, but requires centralized computations. This motivates the main result, which consists in proposing a novel distributed algorithm and proving its convergence to a location equilibrium. The algorithm can be interpreted as natural dynamics describing how the agents move on the network to achieve a location equilibrium. The findings are applied to a numerical study of area coverage for taxi drivers in Hong Kong.