scholarly journals Linear programming models to solve fully fuzzy two person zero sum matrix game

2020 ◽  
Vol 8 (3) ◽  
pp. 775-781
Author(s):  
Ganesh Kumar ◽  
Vinod Jangid
Keyword(s):  
Linear Programming ◽  
Programming Models ◽  
Matrix Game ◽  
Zero Sum

scholarly journals Max-min solution approach for multi-objective matrix game with fuzzy goals

2016 ◽  
Vol 26 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Sandeep Kumar
Keyword(s):  
Linear Programming ◽  
Linear Programming Problem ◽  
Optimization Problem ◽  
Matrix Game ◽  
Game Model ◽  
Solution Approach ◽  
Multi Objective ◽  
Fuzzy Goals ◽  
Fuzzy Goal ◽  
Zero Sum

In this paper, we consider a multi-objective two person zero-sum matrix game with fuzzy goals, assuming that each player has a fuzzy goal for each of the payoffs. The max-min solution is formulated for this multi-objective game model, in which the optimization problem for each player is a linear programming problem. Every developed model for each player is demonstrated through a numerical example.

LEXICOGRAPHIC METHOD FOR MATRIX GAMES WITH PAYOFFS OF TRIANGULAR FUZZY NUMBERS

2008 ◽  
Vol 16 (03) ◽  
pp. 371-389 ◽  
Author(s):  
DENG-FENG LI
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Order Relation ◽  
Programming Models ◽  
Matrix Game ◽  
Triangular Fuzzy Numbers ◽  
Matrix Games ◽  
Lexicographic Method

The purpose of the paper is to study how to solve a type of matrix games with payoffs of triangular fuzzy numbers. In this paper, the value of a matrix game with payoffs of triangular fuzzy numbers has been considered as a variable of the triangular fuzzy number. First, based on two auxiliary linear programming models of a classical matrix game and the operations of triangular fuzzy numbers, fuzzy optimization problems are established for two players. Then, based on the order relation of triangular fuzzy numbers the fuzzy optimization problems for players are decomposed into three-objective linear programming models. Finally, using the lexicographic method maximin and minimax strategies for players and the fuzzy value of the matrix game with payoffs of triangular fuzzy numbers can be obtained through solving two corresponding auxiliary linear programming problems, which are easily computed using the existing Simplex method for the linear programming problem. It has been shown that the models proposed in this paper extend the classical matrix game models. A numerical example is provided to illustrate the methodology.

Solving Two-Person Zero-Sum Game by Matlab

2011 ◽  
Vol 50-51 ◽  
pp. 262-265 ◽  
Author(s):  
Yan Mei Yang ◽  
Yan Guo ◽  
Li Chao Feng ◽  
Jian Yong Di
Keyword(s):  
Game Theory ◽  
Linear Programming ◽  
Special Class ◽  
The Other ◽  
Matrix Game ◽  
Matlab Software ◽  
Zero Sum Games ◽  
Programming Techniques ◽  
Zero Sum

In this article we present an overview on two-person zero-sum games, which play a central role in the development of the theory of games. Two-person zero-sum games is a special class of game theory in which one player wins what the other player loses with only two players. It is difficult to solve 2-person matrix game with the order m×n(m≥3,n≥3). The aim of the article is to determine the method on how to solve a 2-person matrix game by linear programming function linprog() in matlab. With linear programming techniques in the Matlab software, we present effective method for solving large zero-sum games problems.

NOTES ON "LINEAR PROGRAMMING TECHNIQUE TO SOLVE TWO-PERSON MATRIX GAMES WITH INTERVAL PAY-OFFS"

2011 ◽  
Vol 28 (06) ◽  
pp. 705-737 ◽  
Author(s):  
DENG-FENG LI
Keyword(s):  
Linear Programming ◽  
Inequality Constraints ◽  
Asia Pacific ◽  
Programming Models ◽  
Matrix Game ◽  
Programming Technique ◽  
Matrix Games ◽  
Lexicographic Method ◽  
Generic Matrix ◽  
Linear Programming Technique

The aim of this note is to point out and correct some vital mistakes in the paper by P K Nayak and M Pal, "Linear programming technique to solve two person matrix (games with interval pay-offs). Asia-Pacific Journal of Operational Research, 26(2), 285–305". Lots of serious mistakes on the definitions, conclusions, models, methods, proofs and computing results have been corrected and modified in this note. We also indicate inappropriate formulations regarding their proposed linear programming models for solving generic matrix games with interval pay-offs and suggest a pair of linear programming models with any minimal acceptance degree of the interval inequality constraints which may be allowed to violate. The lexicographic method is suggested so that a rational and credible solution of the generic matrix game with interval pay-offs can be achieved.

Algorithm for optimal allocation of limited resources based on the game iteration method

2019 ◽  
pp. 89-99
Author(s):  
V. Ya. Vilisov
Keyword(s):  
Optimal Control ◽  
Linear Programming ◽  
Embedded Systems ◽  
Iterative Method ◽  
High Speed ◽  
Optimal Allocation ◽  
Software Implementation ◽  
Limited Resources ◽  
Matrix Game ◽  
Acceptable Accuracy

The article proposes an algorithm for solving a linear programming problem (LPP) based on the use of its representation in the form of an antagonistic matrix game and the subsequent solution of the game by an iterative method. The algorithm is implemented as a computer program. The rate of convergence of the estimates of the solution to the actual value with the required accuracy has been studied. The software implementation shows a high speed of obtaining the LPP solution with acceptable accuracy in fractions or units of seconds. This allows the use algorithm in embedded systems for optimal control.

Mixed Integer Linear Programming Models for Selecting Ground-Level Ozone Control Strategies

2014 ◽  
Vol 19 (6) ◽  
pp. 503-514 ◽  
Author(s):  
Wei-Che Hsu ◽  
Jay M. Rosenberger ◽  
Neelesh V. Sule ◽  
Melanie L. Sattler ◽  
Victoria C. P. Chen
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Control Strategies ◽  
Ground Level ◽  
Programming Models ◽  
Mixed Integer ◽  
Ground Level Ozone ◽  
Ozone Control
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