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Markovian strategies for piecewise deterministic differential games with continuous and impulse controls

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  • This paper is concerned with the Markovian feedback strategies of piecewise deterministic differential games and their applications to business and management decision-making problems that involve multiple agents and continuous and impulse controls. For a class of piecewise deterministic differential games in finite or infinite horizons we formulate conditions for the value functions in the form of quasi-variational inequalities, prove a verification theorem, and derive a criterion for the Markovian regime change in certain case. These results are applied to a technology adoption problem that involves multiple companies engaged in extraction of an exhaustible resource with different technologies. Using the model proposed by Long et al in [16], we show the existence of a pure Markovian strategy and develop an algorithm for computing the solutions.

    Mathematics Subject Classification: Primary: 91A80, 91A23; Secondary: 91B06.


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  • Figure 3.1.  Possible strategies with parameter values given by (3.15)

    Figure 3.2.  Extraction and consumption rates using parameters in (3.15)

    Figure 3.3.  Possible strategies with $ \gamma^2 = 1.6 $ and other parameter values given by (3.15)

    Figure 4.  Extraction and consumption rates when $ \gamma ^{2} $ is changed to 1.6

    Figure 3.5.  Extraction and consumption rates. The blue and red curves on the right are the consumption rates of Companies 1 and 2, respectively

    Figure 3.6.  Extraction and consumption rates when $ \gamma _{2}^{2} $ is changed to 1.2. The blue and red curves on the right are the consumption rates of Companies 1 and 2, respectively

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