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2020 | OriginalPaper | Chapter

Open-Loop Based Strategies for Autonomous Linear Quadratic Game Models with Continuous Updating

Authors : Ildus Kuchkarov, Ovanes Petrosian

Published in: Mathematical Optimization Theory and Operations Research

Publisher: Springer International Publishing

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Abstract

The class of differential games with continuous updating is quite new, there it is assumed that at each time instant, players use information about the game structure (motion equations and payoff functions of players) defined on a closed time interval with a fixed duration. As time goes on, information about the game structure updates. A linear-quadratic case for this class of games is particularly important for practical problems arising in the engineering of human-machine interaction. In this paper, it is particularly interesting that the open-loop strategies are used to construct the optimal ones, but subsequently, we obtain strategies in the feedback form. Using these strategies the notions of Shapley value and Nash equilibrium as optimality principles for cooperative and non-cooperative cases respectively are defined and the optimal strategies for the linear-quadratic case are presented.

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previous chapter On a One-Dimensional Differential Game with a Non-convex Terminal Payoff

next chapter On Iterative Methods for Searching Equilibrium in Pure Exchange Economy with Multiplicative Utilities of Its Agents

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Title: Open-Loop Based Strategies for Autonomous Linear Quadratic Game Models with Continuous Updating
Authors: Ildus Kuchkarov
Ovanes Petrosian
Publisher: Springer International Publishing
Book: Mathematical Optimization Theory and Operations Research
Print ISBN: 978-3-030-49987-7

Electronic ISBN: 978-3-030-49988-4

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-49988-4_15

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