Abstract
We treat the competition between two Internet Service Providers which are distinguished by the Quality of Services that they propose. We model this competition by means of an infinite-horizon discrete-time differential game. The dynamical modeling is due to the presence of investments of the firms. We solve the problem by using several Pontryagin principles for the optimal control problems associated to this differential game. We obtain the existence and the uniqueness of a Markov–Nash equilibrium of this differential game.
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