Zero-Sum Matrix Games

2017 ◽  
pp. 25-34
Keyword(s):  
Matrix Games ◽  
Zero Sum

Resolving Indeterminacy Approach to Solve Multi-Criteria Zero-Sum Matrix Games with Intuitionistic Fuzzy Goals

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 305 ◽  
Author(s):  
M. G. Brikaa ◽  
Zhoushun Zheng ◽  
El-Saeed Ammar
Keyword(s):  
Intuitionistic Fuzzy Set ◽  
Implementation Process ◽  
Fuzzy Programming ◽  
Matrix Game ◽  
Great Success ◽  
Matrix Games ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Goals ◽  
Linear Programming Problems ◽  
Zero Sum

The intuitionistic fuzzy set (IFS) is applied in various decision-making problems to express vagueness and showed great success in realizing the day-to-day problems. The principal aim of this article is to develop an approach for solving multi-criteria matrix game with intuitionistic fuzzy (I-fuzzy) goals. The proposed approach introduces the indeterminacy resolving functions of I-fuzzy numbers and discusses the I-fuzzy inequalities concept. Then, an effective algorithm based on the indeterminacy resolving algorithm is developed to obtain Pareto optimal security strategies for both players through solving a pair of multi-objective linear programming problems constructed from two auxiliary I-fuzzy programming problems. It is shown that this multi-criteria matrix game with I-fuzzy goals is an extension of the multi-criteria matrix game with fuzzy goals. Moreover, two numerical simulations are conducted to demonstrate the applicability and implementation process of the proposed algorithm. Finally, the achieved numerical results are compared with the existing algorithms to show the advantages of our algorithm.

Game theory and its economic applications

2018 ◽  
Author(s):  
Анатолий Сигал ◽  
Anatoliy Sigal
Keyword(s):  
Game Theory ◽  
Matrix Games ◽  
Managerial Decisions ◽  
Combined Application ◽  
Finite Games ◽  
Basic Concepts ◽  
Zero Sum ◽  
Risk Managers ◽  
Large Groups ◽  
Antagonistic Games

The manual describes the main sections of game theory, the basic concepts of the theory of economic risks and the conceptual framework for modeling the process of making managerial decisions in the economy based on the combined application of statistical and antagonistic games. Antagonistic games (AG) are the finite games of two persons with zero sum, i.e. matrix games, with classical antagonistic games called AG, given by completely known matrices, and neoclassical antagonistic games – AG, given by partially known matrices. The manual is intended primarily for masters who study in the direction of training "business information". However, it will be useful for students and postgraduates studying in large groups of areas of training "Economics and Management", "Mathematics and Mechanics", "Management in Technical Systems", as well as scientific and pedagogical workers specializing in the field of the theory of games, risk managers , managers and economists-practitioners.

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

2021 ◽  
Vol 12 (1) ◽  
pp. 115-126
Author(s):  
Hamiden Abd El- Wahed Khalifa ◽  
Pavan Kumar
Keyword(s):  
Decision Making ◽  
Real Life ◽  
Multiple Criteria Decision Making ◽  
Value Added ◽  
Payoff Matrix ◽  
Matrix Games ◽  
Research Article ◽  
General Algebraic Modeling System ◽  
Classical Mathematics ◽  
Zero Sum

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.

On one Saddle Point Search Algorithm for Continuous Linear Games as Applied to Information Security Problems

2020 ◽  
pp. 58-74
Author(s):  
A.Yu. Bykov ◽  
I.A. Krygin ◽  
M.V. Grishunin ◽  
I.А. Markova
Keyword(s):  
Saddle Point ◽  
Relative Error ◽  
Optimization Problems ◽  
Search Algorithm ◽  
The Other ◽  
Matrix Games ◽  
Random Number Generators ◽  
Point Search ◽  
Fixed Solution ◽  
Zero Sum

The paper introduces a game formulation of the problem of two players: the defender determines the security levels of objects, and the attacker determines the objects for attack. Each of them distributes his resources between the objects. The assessment of a possible damage to the defender serves as an indicator of quality. The problem of a continuous zero-sum game under constraints on the resources of the players is formulated so that each player must solve his own linear programming problem with a fixed solution of the other player. The purpose of this research was to develop an algorithm for finding a saddle point. The algorithm is approximate and based on reducing a continuous problem to discrete or matrix games of high dimension, since the optimal solutions are located at the vertices or on the faces of the simplices which determine the sets of players' admissible solutions, and the number of vertices or faces of the simplices is finite. In the proposed algorithm, the optimization problems of the players are sequentially solved with the accumulated averaged solution of the other player, in fact, the ideas of the Brown --- Robinson method are used. An example of solving the problem is also given. The paper studies the dependences of the number of algorithm steps on the relative error of the quality indicator and on the dimension of the problem, i.e., the number of protected objects, for a given relative error. The initial data are generated using pseudo-random number generators

An optimal transmission strategy in zero-sum matrix games under intelligent jamming attacks

2017 ◽  
Vol 25 (4) ◽  
pp. 1777-1789
Author(s):  
Senthuran Arunthavanathan ◽  
Leonardo Goratti ◽  
Lorenzo Maggi ◽  
Francesco de Pellegrini ◽  
Sithamparanathan Kandeepan ◽  
...  
Keyword(s):  
Jamming Attacks ◽  
Matrix Games ◽  
Transmission Strategy ◽  
Zero Sum ◽  
Optimal Transmission Strategy

scholarly journals Strategic Management in Marketing: A Game Theoretic Approach

2021 ◽  
Vol 12 (6) ◽  
pp. 2518-2524
Author(s):  
Vinod Jangid, Gaurav Sharma, Ganesh Kumar
Keyword(s):  
Fuzzy Numbers ◽  
Status Quo ◽  
Theoretic Approach ◽  
Ranking Methods ◽  
Matrix Games ◽  
Fuzzy Matrix ◽  
Game Theoretic ◽  
Zero Sum ◽  
Determining Factor ◽  
Game Theoretic Approach

In marketing, a real-world dilemma emerging between two rivals, McDonald's and Burger King, is investigated. Both firms use three strategies: discounted pricing, status quo, and aggressive commercial. In such cases, ambiguity is a determining factor. To deal with confusion in payoffs, octagonal fuzzy numbers are used. To rank fuzzy numbers, the average of odd positions, average of even positions, and quartile deviations are used. To solve the reduced modelled two competitors zero sum fuzzy matrix games, the proposed ranking methods are used. Finally, the findings are compared to current approaches that are quite similar to the proposed approach.

scholarly journals Rational Probabilistic Deciders—Part II: Collective Behavior

2007 ◽  
Vol 2007 ◽  
pp. 1-34
Author(s):  
P. T. Kabamba ◽  
W.-C. Lin ◽  
S. M. Meerkov
Keyword(s):  
Collective Behavior ◽  
Steady States ◽  
Minimum Amount ◽  
Reconfigurable Systems ◽  
Exchange Economies ◽  
Matrix Games ◽  
Changing Environments ◽  
Zero Sum ◽  
The Relationship

This paper explores the behavior of rational probabilistic deciders (RPDs) in three types of collectives: zero sum matrix games, fractional interactions, and Edgeworth exchange economies. The properties of steady states and transients are analyzed as a function of the level of rationality,N, and, in some cases, the size of the collective,M. It is shown that collectives of RPDs, may or may not behave rationally, depending, for instance, on the relationship betweenNandM(under fractional interactions) orNand the minimum amount of product exchange (in Edgeworth economies). The results obtained can be useful for designing rational reconfigurable systems that can autonomously adapt to changing environments.

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