On Nonzero-Sum Game Considered on Solutions of a Hybrid System with Frequent Random Jumps

Ilaria Brunetti, Vladimir Gaitsgory () and Eitan Altman
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Ilaria Brunetti: University of Avignon
Vladimir Gaitsgory: Macquarie University
Eitan Altman: INRIA Sophia Antipolis

Dynamic Games and Applications, 2017, vol. 7, issue 3, No 3, 386-401

Abstract: 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.

Keywords: Nonzero-sum game; Slow–fast dynamics; Averaging; Asymptotic Nash equilibrium (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s13235-016-0189-z

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