Doubly invariant equilibria of linear discrete-time games
type: Item
instance of: scholarly article
title: Doubly invariant equilibria of linear discrete-time games
zbMATH Open document ID: 1029.91012
DOI: 10.1016/S0005-1098(02)00063-8
published in: Automatica
publication date: 2002-09-05T00:00:00Z
review text: It is an interesting paper in studing the equilibrium of the class of two persons linear dynamic games in discrete time, in which the perfect state information, feedback strategies and a performance criterion are specified not in terms of payoffs but by two sets in the state space one for each player, each player tries to keep the state in the region of the state space independently of the action of the rival player. The authors define a doubly invariant DI equilibrium. It is obtained when these sets exhibit a double invariance property. The notion of a DI equilibrium links with the Nash equilibrium concept in game theory and with the viability concept in control. The paper gives in 5 sections existence conditions, criteria and algorithms for the determination of DI equilibria of linear dynamic games in discrete time. Two examples illustrate the results are given. I think that it will be useful for the readers to consult the paper ``On discrete dynamical systems associated to games'' by \textit{E. Ahmed} and \textit{A. S. Hegazi} in Adv. Complex Syst. 423-430 (1999).
Mathematics Subject Classification ID: 91A50
Mathematics Subject Classification ID: 91A25
Mathematics Subject Classification ID: 90B25
zbMATH DE Number: 1797134
zbMATH Keywords: controlled invariance
zbMATH Keywords: doubly invariant equilibrium
zbMATH Keywords: Nash equilibrium
zbMATH Keywords: discrete-time dynamic games
zbMATH Keywords: fault tolerance-macroeconomics
author: Paolo Caravani
author: Elena De Santis
reviewed by: Ahmed Hegazi
MaRDI profile type: Publication
cites work: Q3858773
cites work: Viability theory
cites work: Q4317892
cites work: Q4953382
cites work: Double invariance: A new equilibrium concept for two-person dynamic games
cites work: A polytopic game
cites work: Nonlinear state feedback for \(\ell^ 1\) optimal control
cites work: Optimization of the l/sup ∞/-induced norm under full state feedback
description: scientific article; zbMATH DE number 1797134