We consider a situation, in which a regulator believes that constraining a good, created jointly by competitive agents, is socially desirable. Individual levels of outputs, which generate the constrained amount, can be computed as a Pareto-efficient solution of the agents’ joint utility maximisation problem. However, generically, a Pareto-efficient solution is not an equilibrium. We suggest the regulator should calculate a Nash-Rosen coupled-constraint equilibrium (or a “generalised” Nash equilibrium) and use the coupled-constraint Lagrange multiplier to formulate a threat, under which the agents would play a decoupled Nash game. An equilibrium of this game will possibly coincide with the Pareto-efficient solution. We focus on situations when the constraint is saturated, and examine under which conditions a match between an equilibrium and a Pareto solution is possible. We illustrate our ﬁndings using a model for a coordination problem, in which ﬁrms’ outputs depend on each other and where the output levels are important for the regulator.
How to use Rosen’s normalised equilibrium to enforce a socially desirable Pareto efficient solution
14 January 2014