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

Abstract

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.

Study of Carbon Reduction and Marketing Decisions with the Envisioning of a Favorable Event under Cap-and-Trade Regulation

“…They deal with the stochastic optimal control problem where randomness is essentially concentrated in the stopping time terminating the process by applying maximum principle and dynamic programming techniques. The basic thought adopted is to turn the stochastic control problem into the deterministic problem; then, the study of this control problem is extended to the differential game model [54][55][56][57][58]. Since the Markov process is desirable to depict the randomly occurring event, the method is widely adopted in the study of an unexpected event and corresponding impacts, such as potential competitive entry [59][60][61][62], a product recall crisis [26,63,64], climate change or environmental disaster prevention [65][66][67], and the impact of the COVID-19 pandemic [68].…”