Carathéodory's method for a class of dynamic games.
type: Item
instance of: scholarly article
title: Carathéodory's method for a class of dynamic games.
zbMATH Open document ID: 1038.91016
DOI: 10.1016/S0022-247X(02)00276-7
author: Dean A. Carlson
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-02-11T00:00:00Z
review text: The author gives an overview of Carathéodory method and he proves a verification theorem for nonzero sum games. The suppositions of the main theorem (verifications) assume the differentiability of the value functions. Existence results of feedback Nash equilibria (without assuming the differentiability of the values) can be found in [\textit{A. F. Konomenko}, Sov. Math., Dokl. 17, 1557--1560 (1977; Zbl 0366.90141); \textit{A. F. Kleimenof}, Nonantagonistic differential games, Nauk. Ural. Otdelenie, Ekaterinburg (1993)]. At the end two examples of linear quadratic games are discussed.
reviewed by: Marc Quincampoix
Mathematics Subject Classification ID: 91A23
Mathematics Subject Classification ID: 91A25
Mathematics Subject Classification ID: 49N70
zbMATH DE Number: 1866764
zbMATH Keywords: verification theorem for nonzero sum games
zbMATH Keywords: Dynamic games
zbMATH Keywords: Dynamic programming
zbMATH Keywords: Carathéodory's method
zbMATH Keywords: Infinite horizon
zbMATH Keywords: Overtaking Nash equilibrium
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1866764