Decisions in Economics and Finance

, Volume 40, Issue 1–2, pp 317–333 | Cite as

A differential game in a duopoly with instantaneous incentives

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Abstract

In this paper, we study a differential game in which two competing firms exploit a public renewable resource that is relevant from a landscape point of view. We consider a policy maker that provides an instantaneous incentive to the firms in order to prevent the resource exhaustion during the whole extraction period, which coincides with the harvesting license period. We compute an open-loop Nash equilibrium of the differential game, showing that it coincides with a linear feedback Nash equilibrium. Finally, we compute the value of the incentive that leads to the maximization of social welfare considering the incentive both as a pure transfer and as a cost.

Keywords

Open-loop Nash equilibrium Feedback Nash equilibrium Resource extraction Finite time horizon Incentives 

Mathematics Subject Classification

91A23 49N90 91A80 91B76 91A10 

JEL Classification

C61 C72 C73 D21 D23 D43 D60 H23 Q20 
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Notes

Acknowledgements

The authors deeply thank the anonymous referees for the useful and constructive comments which made a significant contribution to the improvement of the paper.

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Copyright information

© Springer-Verlag Italia 2017

Authors and Affiliations

  1. 1.Dipartimento di EconomiaUniversità degli Studi di FoggiaFoggiaItaly
  2. 2.Dipartimento di Scienze aziendali, economiche e metodi quantitativiUniversità degli Studi di BergamoBergamoItaly

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