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International Journal of Modern Education and Computer Science (IJMECS)

ISSN: 2075-0161 (Print), ISSN: 2075-017X (Online)

Published By: MECS Press

IJMECS Vol.10, No.4, Apr. 2018

Stochastic Game with Lexicographic Payoffs

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Author(s)

Mindia E. Salukvadze, Guram N. Beltadze

Index Terms

Lexicographic;Stochastic game;Equilibrium situation;Affine game

Abstract

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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