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Volume 1, Issue 1, May 2016, Page: 5-9
A Matrix Representation of an n-Person 0-1 Game and Its 0-1 Tail Algorithm to Find (Strictly) Pure Nash Equilibria
Dianyu Jiang, Institution of Game Theory and Its Application, Huaihai Institute of Technology, Lianyungang, China
Received: Apr. 2, 2016;       Accepted: Apr. 11, 2016;       Published: May 9, 2016
Abstract
An n-person double action game, i.e., an n-person strategy game, i.e., every player has and only has two actions, is a typical and useful game. It has been proved that in an n-person double game, every player’s two actions can be denoted by 0 and 1. An n-person double action game, i.e., every player’s action set is denoted as {0,1}, is said to be an n-person 0-1 game. In this paper, we first give a matrix representation of an n-person 0-1 game and then give a new and simpler algorithm to find all the (strictly) pure Nash equilibria for an n-person 0-1 game, called 0-1 tail algorithm. Specially, this algorithm can be simplified if the game is symmetrical. Some examples are given to show the algorithm.
Keywords
n-person Double Action Game, n-person 0-1 Game, Symmetry, Matrix Representation, 0-1 Tail Algorithm, Symmetrical 3-person PD, Symmetrical 3-person Game of Rational Pigs
Dianyu Jiang, A Matrix Representation of an n-Person 0-1 Game and Its 0-1 Tail Algorithm to Find (Strictly) Pure Nash Equilibria, Mathematics and Computer Science. Vol. 1, No. 1, 2016, pp. 5-9. doi: 10.11648/j.mcs.20160101.12
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