# Optimal taxation in a common resource oligopoly game

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## Abstract

In this paper, we study the optimal tax policy in a differential oligopoly game where the competing firms share the access to a productive renewable resource. We show that, in a Feedback Nash Equilibrium of the game, a linear Markov tax, imposed on the output, and specified as an affine function of the available resource stock, leads the competing firms to produce the socially optimal quantities over time, thus overcoming the dynamic interplay between the *tragedy of the commons* and the firms’ market power. The optimal tax turns out to be independent from the resource stock in a monopoly, and it cannot be defined in a duopoly.

## Keywords

Tragedy of the commons Renewable resource oligopoly Differential game Optimal tax policy Linear Markov tax## JEL Classification

C61 C72 C73 D21 D23 D43 D62 H21 H23 Q20 Q28## Notes

### Acknowledgements

The author deeply thanks Hassan Benchekroun, Roberto Cellini, Luca Colombo, Luca Grilli, Paola Labrecciosa and Santiago Rubio for many helpful comments, and Guiomar Martin-Herran for her kind invitation to present this paper at the 18th ISDG (International Symposium on Dynamic Games and Applications, Grenoble, France, July 9–12, 2018). This version has benefited from comments and suggestions from the Editor and two anonymous referees.

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