Optimum strategies for two large systems in a multistep game
type: Item
instance of: scholarly article
title: Optimum strategies for two large systems in a multistep game
zbMATH Open document ID: 0607.90092
author: V. I. Grishin
author: N. V. Efimova
published in: Automation and Remote Control
publication date: 1986-01-01T00:00:00Z
review text: The contents and presentation (which may have been hampered by the translation into English somewhat) are poor. The only message of the paper is an algorithm which calculates the saddlepoint of a continuously differentiable, bounded and strictly convex (in u)-concave (in v) function w; here \(u\in {\mathbb{R}}^ n\), \(v\in {\mathbb{R}}^ m\). The algorithm calculates a sequence \((u^{(i)},v^{(i)})\), \(i=1,2,...\). Given \(v^{(i)}\) one determines \(u^{(i+1)}\) by minimizing \(w(u,v^{(i)})\) with respect to u and subsequently one determines \(v^{(i+1)}\) by maximizing \(w(u^{(i+1)},v)\) with respect to v. A proof of the convergence to the saddlepoint is given. Instead of u (v) the authors use the notation K(x) (K(y)), but the role of x respectively y is not clear to the reviewer; they are no state vectors, since state vectors for the two interacting systems are given by X and Y. Constraints on the controls are present; they are introduced as the ''effort distribution is finite'', i.e. bounded by one. The title of the paper and the last sentence of the introduction (''the aim of this work is the determination of an optimal control for operation of a large stochastic system in a multistep game problem of large dimension'') promise a lot. It is disappointing that the multistep character and the stochastic behaviour do not play any role in the paper. Also the largeness of the dimension is mentioned in a few places but not discussed at all.
Mathematics Subject Classification ID: 91A05
Mathematics Subject Classification ID: 90C90
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 3982946
zbMATH Keywords: continuously differentiable bounded strictly convex payoff function
zbMATH Keywords: algorithm
zbMATH Keywords: saddlepoint
reviewed by: Geert Jan Olsder
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3982946