Stochastic Game with Lexicographic Payoffs

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Mindia E. Salukvadze 1,* Guram N. Beltadze 2

1. Georgian National Academy of Sciences, Georgian Technical University, Georgia, Tbilisi

2. Departaments Control Systems and Artifical Intelligence Georgian Technical University, Georgia, Tbilisi, 0175, str. Kostava 77

* Corresponding author.


Received: 22 Dec. 2017 / Revised: 5 Jan. 2018 / Accepted: 30 Jan. 2018 / Published: 8 Apr. 2018

Index Terms

Lexicographic, Stochastic game, Equilibrium situation, Affine game


Stochastic games are discussed as a priva-te class of a general dynamic games. A certain class of lexicographic noncooperative games is studied - lexi-cographic stochastic matrix games . The problem of the existence of Nash equilibrium is studied with two analyses - standard and nonstandard way. Standard means using the same kind of mixed strategies in case of scalar games. In this case in lexi-cographic stochastic matrix game Nash equilibrium may not be existed. Its existence takes place in relevant stochastic affine matrix game to the existence of Nash equilibrium. In game a set of Nash equi-librium is given by means of relevant stochastic affine matrix game's set of equilibrium. The sufficient condi-tions of the existance such affine game is proved. In nonstandard way of analyses we use such mixed stra-tegies, they use components with lexicog-raphic probabilites. In this case the kinds of subsets of a set of equilibrium in game are described.

Cite This Paper

Mindia E. Salukvadze, Guram N. Beltadze, " Stochastic Game with Lexicographic Payoffs", International Journal of Modern Education and Computer Science(IJMECS), Vol.10, No.4, pp. 10-17, 2018. DOI:10.5815/ijmecs.2018.04.02


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