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How to use Rosen's normalised equilibrium to enforce a socially desirable Pareto efficient solution

  • Jacek B. Krawczyk
  • Mabel Tidball

We consider a situation, in which a regulator believes that constraining a complex good created jointly by competitive agents, is socially desirable. Individual levels of outputs that generate the constrained amount of the externality 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 calculates a Nash-Rosen coupled-constraint equilibrium (or a “generalised” Nash equilibrium) and uses the coupled-constraint Lagrange multiplier to formulate a threat, under which the agents will play a decoupled Nash game. An equilibrium of this game will possibly coincide with the Pareto efficient solution. We focus on situations when the constraints are 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.

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Paper provided by LAMETA, Universtiy of Montpellier in its series Working Papers with number 09-20.

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Length: 19 pages
Date of creation: Dec 2009
Date of revision: Jan 2011
Handle: RePEc:lam:wpaper:09-20
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