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Decisions in Economics and Finance

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13-04-2017

A differential game in a duopoly with instantaneous incentives

Authors: Luca Grilli, Michele Bisceglia

Published in: Decisions in Economics and Finance | Issue 1-2/2017

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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.

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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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Title: A differential game in a duopoly with instantaneous incentives
Authors: Luca Grilli
Michele Bisceglia
Publication date: 13-04-2017
Publisher: Springer Milan
Published in: Decisions in Economics and Finance / Issue 1-2/2017
Print ISSN: 1593-8883
Electronic ISSN: 1129-6569
DOI: https://doi.org/10.1007/s10203-017-0189-5

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