Non-linear Incentive Equilibrium Strategies for a Transboundary Pollution Differential Game

  • Javier de Frutos
  • Guiomar Martín-HerránEmail author
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 280)


In this paper we apply non-linear incentive strategies to sustain over time an agreement. We illustrate the use of these strategies in a linear-quadratic transboundary pollution differential game. The incentive strategies are constructed in such a way that in the long run the pollution stock (the state variable) is close to the steady state of the pollution stock under the cooperative mode of play. The non-linear incentive functions depend on the emission rates (control variables) of both players and on the current value of the pollution stock. The credibility of the incentive equilibrium strategies is analyzed and the performance of open-loop and feedback incentive strategies is compared in their role of helping to sustain an agreement over time. We present numerical experiments to illustrate the results.


Incentive equilibria Differential games Credibility Environmental Economics 



We are grateful to two anonymous reviewers for valuable comments and suggestions in an earlier draft of this paper. This research is partially supported by MINECO under projects MTM2016-78995-P (AEI) (Javier de Frutos) and ECO2014-52343-P and ECO2017-82227-P (AEI) (Guiomar Martín-Herrán) and by Junta de Castilla y León VA024P17 and VA105G18 co-financed by FEDER funds (EU).


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.IMUVA and Dpto. Matemática Aplicada, Facultad de CienciasUniversidad de ValladolidValladolidSpain
  2. 2.IMUVA and Dpto. Economía Aplicada, Facultad de Ciencias Económicas y EmpresarialesUniversidad de ValladolidValladolidSpain

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