Differential Antagonistic Games with Lexicographic Vector-Payoffs

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Guram N. Beltadze 1,*

1. Departament Artifical Intelligence Georgian Technical University, Georgia, Tbilisi, 0175, str. Kostava 77

* Corresponding author.

DOI: https://doi.org/10.5815/ijmecs.2019.03.04

Received: 30 Dec. 2018 / Revised: 10 Jan. 2019 / Accepted: 20 Jan. 2019 / Published: 8 Mar. 2019

Index Terms

Lexicographic, Antagonistic, Differential game, Equilibrium, e-equilibrium


In this paper the existence problem of the equilibrium situation in differential antagonistic games with perfect information and lexicographic payoffs or in a  -dimensional vector-payoffs' game where criteria are strictly ranged with preference relation is studied. The players' dinamic is defined by vector differential x=ft,x ,u ),y=gt,y ,v )   equations, respectively control functions u( .), v(. ) and 0.Ttime  interval. This is a game ΓL(x0, y0)=(Γ1,...Γm ) where x0, y0 are starting positions in t=0 moment respectively the first and second players'. x(t)and y(t) are trajectories, the players final aim is finding their optimal variants. A lexicographic ε -equilibrium situation is defined in the game and the conditions of its existence are investiga-terd. These conditions are mainly about f and g  functi-ons. The main definitions are introduced and some results are formulated from theory of differential games with scalar payoff functions and independent move-ments, they are the main for getting results for analogic differential games in the case of lexicographic payoffs. Some auxiliary statements correctness are also establi-shed, on its basic it is proved that in ΓL(x0, y0) game for any ε>0  there exists a lexicographic ε-equilibrium situation in pure strategies. 

Cite This Paper

Guram N. Beltadze, " Differential Antagonistic Games with Lexicographic Vector-Payoffs", International Journal of Modern Education and Computer Science(IJMECS), Vol.11, No.3, pp. 23-30, 2019.DOI: 10.5815/ijmecs.2019.03.04


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