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Robust Nash Equilibrium in multi‐model LQ differential games: analysis and extraproximal numerical procedure
Author(s) -
JiménezLizárraga Manuel,
Poznyak Alex
Publication year - 2007
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.795
Subject(s) - nash equilibrium , differential game , best response , epsilon equilibrium , mathematical economics , differential (mechanical device) , mathematics , simplex , solution concept , correlated equilibrium , mathematical optimization , equilibrium selection , repeated game , computer science , game theory , combinatorics , physics , thermodynamics
This paper tackles the problem of finding a Nash equilibrium for a multi‐model differential game. Player's dynamics is governed by an ordinary differential equation with unknown parameters (Multi‐Model Representation) from a given finite set. The problem consists in the designing of min–max strategies for each player which guarantee an equilibrium for the worst‐case scenario. Based on the Robust Maximum Principle necessary conditions for a game to be in Robust Nash Equilibrium are derived. The LQ differential games are considered in detail. It is shown that the initial min–max differential game may be converted into a standard static game given in a multi‐dimensional simplex. A numerical procedure for resolving the LQ differential game is designed. Copyright © 2007 John Wiley & Sons, Ltd.