Newton’s Method, Bellman Recursion and Differential Dynamic Programming for Unconstrained Nonlinear Dynamic Games

Dynamic games arise when multiple agents with differing objectives control a dynamic system. They model a wide variety of applications in economics, defense, energy systems and etc. However, compared to single-agent control problems, the computational methods for dynamic games are relatively limited...

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Vydáno v:Dynamic games and applications Ročník 12; číslo 2; s. 394 - 442
Hlavní autoři: Di, Bolei, Lamperski, Andrew
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.06.2022
Springer Nature B.V
Témata:
Algorithms
Approximation
Communications Engineering
Computer Systems Organization and Communication Networks
Dynamic programming
Dynamical systems
Economic models
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Game Theory
Games
Management Science
Mathematics
Mathematics and Statistics
Multiagent systems
Networks
Nonlinear dynamics
Operations Research
Optimal control
Social and Behav. Sciences
Noncooperative dynamic games
Feedback Nash equilibrium
Newton’s method
Differential dynamic programming
Open-loop Nash equilibrium
ISSN:2153-0785, 2153-0793
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Popis
Shrnutí:Dynamic games arise when multiple agents with differing objectives control a dynamic system. They model a wide variety of applications in economics, defense, energy systems and etc. However, compared to single-agent control problems, the computational methods for dynamic games are relatively limited. As in the single-agent case, only specific dynamic games can be solved exactly, so approximation algorithms are required. In this paper, we show how to extend the Newton step algorithm, the Bellman recursion and the popular differential dynamic programming (DDP) for single-agent optimal control to the case of full-information nonzero sum dynamic games. We show that the Newton’s step can be solved in a computationally efficient manner and inherits its original quadratic convergence rate to open-loop Nash equilibria, and that the approximated Bellman recursion and DDP methods are very similar and can be used to find local feedback O ( ε 2 ) -Nash equilibria. Numerical examples are provided.
Bibliografie:ObjectType-Article-1
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ISSN:2153-0785
2153-0793
DOI:10.1007/s13235-021-00399-8