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.
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Notes
For a formal definition of a differential game with fixed time horizon, see Basar and Olsder (1999).
For technical requirements about the feasibility of a pair of open-loop strategies, see again Basar and Olsder (1999).
Please note that the parameter A represents the so-called market dimension, i.e., the number of final products that could be sold if the price was equal to zero, hence it is reasonable to assume: \(A\gg 1\).
Note that second-order conditions are satisfied since the expression to be maximized in (6) is concave in \(\phi _i\).
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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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Grilli, L., Bisceglia, M. A differential game in a duopoly with instantaneous incentives. Decisions Econ Finan 40, 317–333 (2017). https://doi.org/10.1007/s10203-017-0189-5
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DOI: https://doi.org/10.1007/s10203-017-0189-5