A Study on Non cooperative Games Under Inexact Environment

Abstract

The prime intent of this thesis is to narrate the theoretical framework of non-cooperative newlinegames under several inexact environments and their implementation in reality. Game newlinetheory has diverse applications in different disciplines, such as business studies, politics, newlineindustries, economics, computer science, medical science, international relations, etc. newlineIn reality, due to different parameters, information is gathered in imprecise form. This newlinephenomenon inspires us to assess the payoffs in different appropriate extensions of fuzzy newlinesets. newlineTo the best of our knowledge, there is a lot of work in the fuzzy or the intuitionistic newlinematrix and bimatrix games. But, in fuzzy games, only the degree of acceptance of the newlineplayers toward the information are counted while in the intuitionistic fuzzy games, both newlinethe degree of acceptance and the degree of non-acceptance of the players toward the newlineinformation are collected. But these two extensions of matrix games are not sufficient to newlinecope up with all kind of inadequacies and impreciseness. To cover that gap, we incarnate newlinea matrix game in the several extensions of hesitant fuzzy background. newlineIn matrix games, due to lack of information and lack of attention of players toward newlinethe information, there always exists some hesitancy. Neither fuzzy set nor IFS are sufficient newlineto describe payoff values. This gap us to imply the concept of hesitant fuzzy sets newlinein matrix games. The elements of the payoff matrix are represented by triangular hesitant newlinefuzzy elements. To make the solution we derive two hesitant fuzzy programming newlineproblems. Applying the score function of hesitant fuzzy elements we transform these newlinetwo programming problems into two triangular fuzzy non-linear programming problems. newlineThen we utilize the concept of the Lexicographic method to determine the optimal newlinestrategies and the value of the game for the players. newline