Electricity markets with flexible consumption as nonatomic congestion games

This article studies nonatomic congestion games with symmetric players sending flow in arcs linking a unique source and destination. These games can represent systems where electricity retailers controlling flexible consumption minimize their energy costs. We focus on games with affine cost functions and define laminar Nash equilibrium where the constraints on the minimum and maximal flow that a player must send in a given arc are not binding. We show that the flow sent by a player at a laminar Nash equilibrium does not depend on the demand of other players. In laminar flow, we bound the price of anarchy and the ratio between the maximum and the minimum arc cost. Finally, we propose a simple method based on the property of a laminar Nash equilibrium to compute the price of flexibility to which energy flexibility should be remunerated in electric power systems.