Optimal Solutions For Non-cooperative Games Under Uncertainty

Game theory is an important research area of operation research,which mainly concerns with competitive and skillful interaction between the rational,intelligent decision-makers.After the pioneering work of Neumann and Morgenstern(1953),game theory has been successfully applied to many fields,such as political vote,biological evolutionism,online shopping marketing problems,management science,operational research,economics,finance,business,social science,engineering,and water management.Game theory effectively affects the hypothesis of economics,financial aspects,and the literature on applying game theoretical and related ways to economics is developing exponentially,yet numerous hypothetical and observational challenges remain in this field.The main causes of these theoretical-empirical challenges are due to the environments under realization.Due to the complexity of real-life situations,uncertainties arise to determine the parameters information in most of the practical problems.This imprecision/uncertainty is inevitable and hence the data is not precise all the time and is given as estimates.These types of uncertainties are difficult to tackle by classical set or crisp set.To overcome these situations,several uncertain environments such as fuzzy environment,intuitionistic fuzzy environment,dual hesitant environment,neutrosophic environment,rough interval environment,fuzzy rough environment,etc.are introduced.The thesis aims to explore the non-cooperative game?s problems under the shadow of different uncertain environments and establishes simple,efficient,and effective solution methodologies to solve these problems expertly and decently.The all possible outcomes of the players in game are arranged and displayed in matrix or matrices,termed as payoff matrix or matrices with elements as payoff elements.In this thesis,the payoff elements are defined under uncertainty with various types of uncertain environments with their pros and cons and applicability in real-world examples.In this dissertation,six optimization problems in non-cooperative games problems under different uncertain environments are discussed.The first problem is the multi-criteria zero-sum matrix game with intuitionistic fuzzy goals,a generalization of the multi-criteria matrix game with fuzzy goals.A new indeterminacy resolving approach is incorporated to obtain Pareto optimal security strategies for both players.A numerical simulation is incorporated to demonstrate the applicability and implementation process of the proposed algorithm.The achieved numerical results are compared with the existing algorithms to show the advantages of our algorithm.The second problem is the two-person zero-sum matrix games with payoffs of single-valued trapezoidal neutrosophic numbers.A newly proposed Ambika technique,the related advantages and disadvantages with others are described.Thereafter,an experimental analysis is incorporated to expose the efficiency and effectiveness of our proposed study,and the obtained results are compared.The third problem is the constrained bi-matrix games in single valued trapezoidal neutrosophic entities.A new ranking function based on the-cut of neutrosophic set and is applied on constrained bi-matrix game model by validating real-life problem.Moreover,a comparative study is explored among the other existing techniques.In the fourth problem,a two-person zero-sum game phenomenon in triangular dual hesitant fuzzy numbers environment is designed.The flaws of the existing approach to such problem are pointed out.Moreover,to resolve these flaws,a novel,general and corrected approach called the Mehar approach is proposed to obtain the optimal strategies for triangular dual hesitant fuzzy matrix games.In this approach,it is verified that any matrix game with triangular dual hesitant fuzzy numbers payoffs always has a triangular dual hesitant fuzzy numbers equilibrium value.Application example is provided to demonstrate the applicability of the proposed methodology,and the achieved results are compared with the existing method.The fifth problem is bi-matrix games with rough intervals payoffs.Two approaches are presented to solve the proposed problem and corresponding results are compared.An experimental analysis is incorporated to expose the efficiency and effectiveness of our proposed study in reality.In the sixth problem,a novel constraint matrix games with payoffs of fuzzy rough numbers is designed.A new fuzzy multi-objective programming algorithm is incorporated to get the optimal solutions.This algorithm proves that constrained matrix game with fuzzy rough payoffs has a fuzzy rough-type game value.Moreover,the effectiveness and reasonableness of the proposed algorithm are demonstrated by a real example of the market share game problem.