On the Structure and Regularity of Optimal Solutions in a Differential Game with Regime Switching and Spillovers

Bondarev, Anton; Gromov, Dmitry

doi:10.1007/978-3-030-54576-5_8

Cited by 2 publications

(1 citation statement)

References 25 publications

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“…Somewhat different approaches were pursued in Matveev, 1999, 2000;Zelikin et al, 2017), who also studied cyclic systems and proved the existence of HLCs, but did not investigate their optimality. In a recent paper (Reddy, Schumacher and Engwerda, 2020) (see also Bondarev and Gromov (2021) and Seidl (2019)), a discounted hybrid optimal control problem (DHOCP) with control switches determined by the state (state-driven switching using the terminology from Gromov and Gromova (2017)) was studied, and it was shown that such a problem cannot have an HLC as an optimal solution. In contrast to the mentioned case, we consider a DHOCP with time-driven switching (a system that undergoes regime changes at fixed time instants).…”

Section: Introductionmentioning

confidence: 99%

Optimality and sustainability of hybrid limit cycles in the pollution control problem with regime shifts

Громов¹,

Shigoka²,

Bondarev³

2022

Preprint

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In this paper, we consider the problem of pollution control in a system that undergoes regular regime shifts. We first show that the optimal policy of pollution abatement is periodic as well, and is described by the unique hybrid limit cycle. We next introduce the notion of an environmentally sustainable solution, and demonstrate that such a policy is the only one that yields the best possible trade-off between steadily achieving profit and ensuring environmental preservation. In contrast to that, the policy that is not environmentally sustainable eventually enters stagnation. To further illustrate our findings, we compare the optimal periodic solution with a myopic one. Interestingly enough, the myopic solution yields higher overall payoff in the short-run, but completely fails in the long-run, while the environmentally sustainable policy yields maximal payoff and preserves the environment over the infinite time interval.

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