A method to solve two-player zero-sum matrix games in chaotic environment

This research article proposes a method for solving the two-player zero-sum matrix games in chaotic environment. In a fast growing world, the real life situations are characterized by their chaotic behaviors and chaotic processes. The chaos variables are defined to study such type of problems. Classical mathematics deals with the numbers as static and less value-added, while the chaos mathematics deals with it as dynamic evolutionary, and comparatively more value-added. In this research article, the payoff is characterized by chaos numbers. While the chaos payoff matrix converted into the corresponding static payoff matrix. An approach for determining the chaotic optimal strategy is developed. In the last, one solved example is provided to explain the utility, effectiveness and applicability of the approach for the problem.Abbreviations: DM= Decision Maker; MCDM = Multiple Criteria Decision Making; LPP = Linear Programming Problem; GAMS= General Algebraic Modeling System

(R1976) A Novel Approach to Solve Fuzzy Rough Matrix Game with Two Players

This paper proposes a new method for solving a two-person zero-sum fuzzy matrix game with goals, payoffs, and decision variables represented as triangular fuzzy rough numbers. We created a pair of fully fuzzy rough linear programming problems for players. Triangular fuzzy rough numbers can be used to formulate two fuzzy linear programming problems for the first player in the form of upper approximation intervals and lower approximation intervals. Two problems for the second player can be created in the same way. These problems have been split into five sub-crisp problems for the player first and five sub-crisp problems for the player second. The solution to the game can be obtained by solving these ten fuzzy linear programming problems. To demonstrate the method, a numerical example is provided. Using Wolfram Cloud, optimal strategies and game values are calculated for various parameters. Sensitivity analysis is carried out by altering the values of parameters

Compromise in cooperative game and the VIKOR method

Five approaches in conflict resolution are distinguished, based on cooperativeness and aggressiveness in resolving conflict. Compromise based on cooperativeness is emphasized here as a solution in conflict resolution. Cooperative game theory oriented towards aiding the conflict resolution is considered and the compromise value for TU(transferable utility)-game is presented. The method VIKOR could be applied to determine compromise solution of a multicriteria decision making problem with noncommensurable and conflicting criteria. Compromise is considered as an intermediate state between conflicting objectives or criteria reached by mutual concession. The applicability of the cooperative game theory and the VIKOR method for conflict resolution is illustrated

A Better Approach for Solving a Fuzzy Multiobjective Programming Problem by Level Sets

In this paper, we deal with the resolution of a fuzzy multiobjective programming problem using the level sets optimization. We compare it to other optimization strategies studied until now and we propose an algorithm to identify possible Pareto efficient optimal solutions

Developing A Group Decision Support System (gdss) For Decision Making Under Uncertainty

Multi-Criteria Decision Making (MCDM) problems are often associated with tradeoffs between performances of the available alternative solutions under decision making criteria. These problems become more complex when performances are associated with uncertainty. This study proposes a stochastic MCDM procedure that can handle uncertainty in MCDM problems. The proposed method coverts a stochastic MCDM problem into many deterministic ones through a Monte-Carlo (MC) selection. Each deterministic problem is then solved using a range of MCDM methods and the ranking order of the alternatives is established for each deterministic MCDM. The final ranking of the alternatives can be determined based on winning probabilities and ranking distribution of the alternatives. Ranking probability distributions can help the decision-maker understand the risk associated with the overall ranking of the options. Therefore, the final selection of the best alternative can be affected by the risk tolerance of the decisionmakers. A Group Decision Support System (GDSS) is developed here with a user-friendly interface to facilitate the application of the proposed MC-MCDM approach in real-world multiparticipant decision making for an average user. The GDSS uses a range of decision making methods to increase the robustness of the decision analysis outputs and to help understand the sensitivity of the results to level of cooperation among the decision-makers. The decision analysis methods included in the GDSS are: 1) conventional MCDM methods (Maximin, Lexicographic, TOPSIS, SAW and Dominance), appropriate when there is a high cooperation level among the decision-makers; 2) social choice rules or voting methods (Condorcet Choice, Borda scoring, Plurality, Anti-Plurality, Median Voting, Hare System of voting, Majoritarian iii Compromise ,and Condorcet Practical), appropriate for cases with medium cooperation level among the decision-makers; and 3) Fallback Bargaining methods (Unanimity, Q-Approval and Fallback Bargaining with Impasse), appropriate for cases with non-cooperative decision-makers. To underline the utility of the proposed method and the developed GDSS in providing valuable insights into real-world hydro-environmental group decision making, the GDSS is applied to a benchmark example, namely the California‘s Sacramento-San Joaquin Delta decision making problem. The implications of GDSS‘ outputs (winning probabilities and ranking distributions) are discussed. Findings are compared with those of previous studies, which used other methods to solve this problem, to highlight the sensitivity of the results to the choice of decision analysis methods and/or different cooperation levels among the decision-maker

A comprehensive review of hybrid game theory techniques and multi-criteria decision-making methods

More studies trend to hybrid the game theory technique with the multi-criteria decision-making (MCDM) method to aid real-life problems. This paper provides a comprehensive review of the hybrid game theory technique and MCDM method. The fundamentals of game theory concepts and models are explained to make game theory principles clear to the readers. Moreover, the definitions and models are elaborated and classified to the static game, dynamic game, cooperative game and evolutionary game. Therefore, the hybrid game theory technique and MCDM method are reviewed and numerous applications studied from the past works of literature are highlighted. The result of the previous studies shows that the fundamental elements for both frameworks were studied in various ways with most of the past studies tend to integrate the static game with AHP and TOPSIS methods. Also, the integration of game theory techniques and MCDM methods was studied in various applications such as politics, economy, supply chain, engineering, water management problem, allocation problem and telecommunication network selection. The main contribution of the recent studies of employment between game theory technique and MCDM method are analyzed and discussed in detail which includes static and dynamic games in the non-cooperative game, cooperative game, both non-cooperative and cooperative games and evolutionary gam

A strategic cooperative game-theoretic model for market segmentation with application to banking in emerging economies

Market segmentation is essential to target efficaciously core-segment customers and to obtain a competitive advantage. Firms when confronted by the range of market segments, have difficulty in deciding the core-segment customers who are the most probable purchasers of their product and services. We propose a novel fuzzy group multi-criteria method for market entry and segment evaluation and selection. This proposed method provides a comprehensive and systematic framework that combines bi-level multi-objective optimization with real option analysis (ROA) and fuzzy cooperative n-person game theory. The contribution of the proposed segment evaluation and selection method is fivefold: (1) it addresses the gaps in the marketing literature on the efficacious and effective assessment of market segments; (2) it provides a comprehensive and systematic framework that combines bi-level multi-objective optimization with ROA and fuzzy cooperative n-person game theory; (3) it considers fuzzy logic and fuzzy sets to represent ambiguous, uncertain or imprecise information; (4) it does not insist on consensus but synthesizes a representative outcome based on qualitative judgments and quantitative data; and (5) it is applicable to national and international market segmentation. The practical application of this proposed framework illustrates the efficacy of the procedures and algorithms

Plural Rationality and Interactive Decision Processes; Proceedings of an IIASA Summer Study on Plural Rationality and Interactive Decision Processes, Sopron, Hungary, August 16-26, 1984

These Proceedings report the scientific results of the Summer Study on Plural Rationality and Interactive Decision Processes organized jointly by IIASA and the Hungarian Committee for Applied Systems Analysis. Sixty-eight researchers from sixteen countries participated, most of them contributing papers or experiments. The Study gathered specialists from many disciplines, from philosophy and cultural anthropology, through decision theory, game theory and economics, to engineering and applied mathematics. Twenty-eight of the papers presented during the Study are included in this volume

A Prospect Theory-Based Real Option Analogy for Evaluating Flexible Systems and Architectures in Naval Ship Design.

A constant trend in U.S. Navy design and acquisition programs has been the emphasis on flexible systems and architectures. Modularity and design-for-upgradability are two examples of this trend. Given the increasing importance of flexibility in Naval design, the methods used for valuing Naval assets should adequately capture the impact of such flexibility. Current static budgetary techniques and net present value (NPV) analysis underestimate the value of the embedded ``optionality'' of flexible design features. The use of real options analysis (ROA) has been proposed to correct this underestimation, however the theory is not universally applicable to the naval domain because of key assumptions made by a real options approach. These deficiencies leave designers and decision makers to rely on their intuition and engineering experience when evaluating flexible systems and architectures. A quantitative evaluation framework would add valuable analytical rigor to increasingly complex designs and demanding mission requirements. This research presents a novel framework for evaluating flexible Naval assets, called prospect theory-based real options analysis (PB-ROA). The framework abstracts the principles of ROA to suit a wide variety of naval applications. Since naval assets do not generate cash flows, utility theory provides the alternative measure of value within PB-ROA. However, without a market where the assets are traded, a new source for data on prevailing risk tolerances in needed to properly adjust the option's value according to uncertainty. Where some prior research relies solely on utility curves to determine risk aversion, PB-ROA uses a unique mechanism inspired by Prospect Theory to derive the risk-adjusted probability measure from the decision maker's marginal utility curve(s). This enables PB-ROA to include the impact of loss aversion where previously it has been ignored. Game theory is also incorporated into PB-ROA to address the unique characteristic of some naval options which may be leveraged to influence the behavior of other agents in the Navy's environment. With game theory, PB-ROA lends a new perspective on the value of ``game changing'' options, which do not simply react to changes in the environment, but exert a feedback effect on it as well.PhDNaval Architecture & Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/107165/1/jtknight_1.pd