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Markovian strategies with continuous and impulse controls for a differential game model of revolution

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  • Weihua Ruan

Abstract

This paper is concerned with a piecewise-deterministic differential game model of political regime changes. We modify and study the model proposed by Boucekkine et al. in [7]. The original model does not allow all players to take full controls as the situation progresses. Hence, it does not lead to closed-loop strategies. We fix the problem by deriving and using a system of quasi-variational inequalities associated with the differential game, and proving a criterion for the regime change. As a result, we find Markovian strategies for all players. A numerical example for illustration of the method is given. Implications of the results to political changes in a society are discussed. Some results are extended to more general models that incorporate gradual and abrupt changes, as well as continuous and impulse controls.

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  • Weihua Ruan, 2021. "Markovian strategies with continuous and impulse controls for a differential game model of revolution," The Journal of Mathematical Sociology, Taylor & Francis Journals, vol. 45(2), pages 79-99, April.
    • Handle: RePEc:taf:gmasxx:v:45:y:2021:i:2:p:79-99
    DOI: 10.1080/0022250X.2020.1726344
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