Journal of Global Optimization

, Volume 70, Issue 2, pp 455–476 | Cite as

Cooperation in pollution control problems via evolutionary variational inequalities



In this paper, we develop a cooperative game framework for modeling the pollution control problem in a time-dependent setting. We examine the situation in which different countries, aiming at reducing pollution emissions, coordinate both emissions and investment strategies to optimize jointly their welfare. We state the equilibrium conditions underlying the model and provide a formulation in terms of an evolutionary variational inequality. Then, by means of infinite dimensional duality tools, we prove the existence of Lagrange multipliers that play a fundamental role to describe countries’ decision-making processes. Finally, we discuss the existence of solutions and provide a numerical example.


Evolutionary variational inequality Infinite dimensional duality Cooperative games Kyoto Protocol 

Mathematics Subject Classification

49J40 49N15 91B50 91B76 



The research was partially supported by INdAM GNAMPA Project 2015 Nuove frontiere dei problemi di equilibrio su rete: dallo sviluppo sostenibile alla dinamica dei disastri ambientali ai crimini informatici. This support is gratefully acknowledged.


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità di CataniaCataniaItaly

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