Numerical solutions to coupled-constraint (or generalised Nash) equilibrium problems

This paper is about games where the agents face constraints in the combined strategy space (unlike in standard games where the action sets are defined separately for each player) and about computational methods for solutions to such games. The motivation examples for such games include electricity generation problems with transmission capacity constraints, environmental management to control pollution and Internet switching to comply to buffers of bounded capacity. In each such problem a regulator may aim at compliance to standards or quotas through taxes or charges. The relevant solution concept for these games has been known under several names like generalised Nash equilibrium, coupled constraint equilibrium and more. Existing numerical methods converging to such an equilibrium will be explained. Application examples of use of NIRA, which is a suite of Matlab routines that implement one of the methods, will be provided.