We consider the general problem of industrial production in a set of countries subject to a common environmental regulation that limits the emissions of specific sectors. Due to these restrictions, the problem is treated as a generalized non-cooperative game where players (countries) have joint (environmental) constraints caused by the necessity of a common and compulsory emission regulation. The problem is to find a natural mechanism for attaining the corresponding generalized equilibrium state. We suggest a share allocation method, which yields a suitable decomposition type procedure and replaces the initial problem with a sequence of non-cooperative games on Cartesian product sets. We also show that its implementation can be simplified essentially after application of a regularized penalty method. In the case study, we take inspiration from the European Union Emission Trading System (EU-ETS) and we introduce an environmental regulation that restricts the carbon emissions of energy, cement, and steel sectors in some European countries. Our results confirm the important role played by energy sector in reducing carbon emissions.
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