Abstract
We study a nonzero-sum game considered on the solutions of a hybrid dynamical system that evolves in continuous time and that is subjected to abrupt changes in parameters. The changes in the parameters are synchronized with (and determined by) the changes in the states–actions of two Markov decision processes, each of which is controlled by a player who aims at minimizing his or her objective function. The lengths of the time intervals between the “jumps” of the parameters are assumed to be small. We show that an asymptotic Nash equilibrium of such hybrid game can be constructed on the basis of a Nash equilibrium of a deterministic averaged dynamic game.
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An essential part of this paper was written while Ilaria Brunetti was visiting the Department of Mathematics of Macquarie University, Sydney, Australia. The work of Vladimir Gaitsgory was supported by the ARC Discovery Grants DP130104432 and DP150100618.
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Brunetti, I., Gaitsgory, V. & Altman, E. On Nonzero-Sum Game Considered on Solutions of a Hybrid System with Frequent Random Jumps. Dyn Games Appl 7, 386–401 (2017). https://doi.org/10.1007/s13235-016-0189-z
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DOI: https://doi.org/10.1007/s13235-016-0189-z