Towards an understanding of tradeoffs between regional wealth, tightness of a common environmental constraint and the sharing rules

Consider a country with two regions that have developed differently so that their current levels of energy efficiency differ. Each region's production involves the emission of pollutants, on which a regulator might impose restrictions. The restrictions can be related to pollution standards that the regulator perceives as binding the whole country (e.g., enforced by international agreements like the Kyoto Protocol). We observe that the pollution standards define a common constraint upon the joint strategy space of the regions. We propose a game theoretic model with a coupled constraints equilibrium as a solution to the regulator's problem of avoiding excessive pollution. The regulator can direct the regions to implement the solution by using a political pressure, or compel them to employ it by using the coupled constraints' Lagrange multipliers as taxation coefficients. We specify a stylised model that possesses those characteristics, of the Belgian regions of Flanders and Wallonia. We analytically and numerically analyse the equilibrium regional production levels as a function of the pollution standards and of the sharing rules for the satisfaction of the constraint. For the computational results, we use NIRA, which is a piece of software designed to min-maximise the associated Nikaido-Isoda function.