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

Weihua Ruan

The Journal of Mathematical Sociology, 2021, vol. 45, issue 2, 79-99

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.

Date: 2021
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DOI: 10.1080/0022250X.2020.1726344

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