# A Complementarity Approach for an Environmental–Economic Game with Coupling Emission Constraints

## Abstract

We consider an environmental–economic game where players face not only Cournot competition but also coupling environmental and individual capacity constraints. Under the complementarity problem framework, we study the existence of the (normalized) Nash equilibrium, computability of the equilibria, and the closed form expressions of the optimal weights. We also report numerical results of two examples as well as the insights gained from them.

## Keywords

Emission cap Cournot competition Complementarity problems Environmental game Lemke’s method## Notes

### Acknowledgements

The authors would like to thank the two anonymous reviewers whose comments have significantly improved the presentation of this paper. The authors are also grateful to the editor-in-chief, Dr. Jerzy A. Filar, for his comments and suggestions that have made the paper much more readable to this journal’s audience.

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