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.

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.

Vector Valued Non Zero Sum Games and Non Linear Programming

OPSEARCH ◽  
1997 ◽  
Vol 34 (3) ◽  
pp. 180-185 ◽  
Author(s):  
M. V. Durga Prasad ◽  
P. C. Sreenivas
Keyword(s):  
Linear Programming ◽  
Non Linear Programming ◽  
Zero Sum Games ◽  
Non Linear ◽  
Zero Sum ◽  
Vector Valued

Finding compromise solutions for fully fuzzy multi-olbjective linear programming problems by using game theory approach

2021 ◽  
pp. 1-11
Author(s):  
Gizem Temelcan ◽  
Hale Gonce Kocken ◽  
Inci Albayrak
Keyword(s):  
Game Theory ◽  
Linear Programming ◽  
Fuzzy Linear Programming ◽  
Theory Approach ◽  
Compromise Solution ◽  
Objective Functions ◽  
Multiobjective Linear Programming ◽  
Trade Off ◽  
Linear Programming Problems ◽  
Zero Sum

Solving multiobjective linear programming (MOLP) problems and fully fuzzy multi-objective linear programming (FFMOLP) problems involves the trade-off process among several objectives. A new algorithm extended where FFMOLP problems are solved using a 2-player zero-sum game approach to deal with this case. Firstly, The FFMOLP problem is separated into a certain number of fully fuzzy linear programming (FFLP) problems and each is solved by applying any method. After forming a ratio matrix, a game theory approach is applied for finding the weights of objective functions and a weighted LP problem is constructed by these weights. Solving the weighted LP problem, a fuzzy compromise solution of the FFMOLP problem is found. Constructing different ratio matrices, it is also possible to obtain more than one compromise solution to be offered to the decision-maker(s). Some examples are given to show the applicability of the algorithm.

scholarly journals On the exact polynomial time algorithm for a special class of bimatrix game

2013 ◽  
Vol 54 ◽  
Author(s):  
Jonas Mockus ◽  
Martynas Sabaliauskas
Keyword(s):  
Game Theory ◽  
Linear Programming ◽  
Nash Equilibrium ◽  
Polynomial Time ◽  
Explicit Solution ◽  
Special Class ◽  
Polynomial Algorithm ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Bimatrix Game

The Strategy Elimination (SE) algorithm was proposed in [2] and implemented by a sequence of Linear Programming (LP) problems. In this paper an efficient explicit solution is developed and the convergence to the Nash Equilibrium is proven.Keywords: game theory, polynomial algorithm, Nash equilibrium.

John von Neumann's Contribution to Modern Game Theory

2004 ◽  
Vol 54 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Ferenc Forgó
Keyword(s):  
Game Theory ◽  
Cooperative Games ◽  
Minimax Theorem ◽  
Stable Set ◽  
Zero Sum Games ◽  
Side Payments ◽  
Basic Concepts ◽  
Definition Of ◽  
Zero Sum ◽  
Abstract Games

The paper gives a brief account of von Neumann's contribution to the foundation of game theory: definition of abstract games, the minimax theorem for two-person zero-sum games and the stable set solution for cooperative games with side payments. The presentation is self-contained, uses very little mathematical formalism and caters to the nonspecialist. Basic concepts and their implications are in focus. It is also indicated how von Neumann's groundbreaking work initiated further research, and a few unsolved problems are also mentioned.

scholarly journals PENERAPAN KONSEP TEORI PERMAINAN (GAME THEORY) DALAM PEMILIHAN STRATEGI KAMPANYE POLITIK (Studi Kasus : Strategi Pemenangan Pemilukada DKI Jakarta Tahun 201

2018 ◽  
Vol 7 (2) ◽  
pp. 173
Author(s):  
AHMAD SAIFUDDIN ◽  
NI KETUT TARI TASTRAWATI ◽  
KARTIKA SARI
Keyword(s):  
High School ◽  
Game Theory ◽  
Zero Sum Games ◽  
Zero Sum

In Game Theory, generally discusses the zero sum games and non-zero sum games. Both of these studies applied in solving problems predicting the chosen decision based capabilities (pay off). In a case study of the preparation and delivery of the election in Jakarta through the application of the concept of the non-zero sum game obtained by the conclutions that AHY – SM and AB – SU has five same optimum strategies: capture East Jakarta voters, women voters, 20 -29 years old voters, graduated from high school voters, and the Javaness community. While BTP – DSH only different in maximizing strategy of capturing men voters and West Jakarta voters.

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