| Peer-Reviewed

A Matrix Representation of an n-Person 0-1 Game and Its 0-1 Tail Algorithm to Find (Strictly) Pure Nash Equilibria

Received: 2 April 2016     Accepted: 11 April 2016     Published: 9 May 2016
Views:       Downloads:
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.

Published in Mathematics and Computer Science (Volume 1, Issue 1)
DOI 10.11648/j.mcs.20160101.12
Page(s) 5-9
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

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

References
[1] Schelling T. C. (1978). Micro-Motives and Macro-Behavior, W. W. Norton, New York.
[2] Molander P. (1992). The prevalence of free riding, Journal of Conflict Resolution. 36: 756-771.
[3] Taylor M. (1995). The Possibility of Cooperation. Cambridge University Press. New York.
[4] Jiborn Magnus (1999). Voluntary Coercion, Collective Action and the Social Contract, Department of Philosophy, Lund University.
[5] Jiang D. Y. (2015a). Situation Analysis of Double Action Games-Applications of Information Entropy to Game Theory. Deutschland/Germany:Lap Lambert Academic Publishing.
[6] Schelling T. C. (1980). The Strategy of Conllict. York: Harvard University Press.
[7] Roger A. McCain (2004). Game Theory: A Non-Technical Introduction to the Analysis of Strategy, Thomson South-Western.
[8] Fabac, R., D. Radoševic & I. Magdalenic (2014). Autogenerator-based modelling framework for development of strategic games simulations: rational pigs game extended. The Scientific World Journal.
[9] Jiang D. Y. (2015b). L-system of Boxed Pigs and its Deductive Sub-systems------Based on Animal and Economic Behavior. Columbia (USA): Columbia International Publishing.
[10] Jiang, D. Y. (2015). Strict descriptions of some typical 2×2 games and negative games. Economics. Special Issue: Axiomatic Theory of Boxed Pigs. 4(3-1): 6-13. DOI 10.11648/ j.eco.s. 2015040301.12.
[11] Li Q., D. Y., Jiang, T. Matsuhisa, Y. B. Shao, X. Y. Zhu (2015). A Game of Boxed Pigs to Allow Robbing Food. Economics. Special Issue: Axiomatic Theory of Boxed Pigs. Vol. 4, No. 3-1, pp. 14-16. doi: 10.11648/j.eco.s.2015040301.13
[12] Jiang D. Y., Y. B. Shao, & X. Y. Zhu (2016). A negative rational pigs game and its applications to website management. Game View. Vol. 2. no. 1. pp. 1-16.
Cite This Article
  • APA Style

    Dianyu Jiang. (2016). 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, 1(1), 5-9. https://doi.org/10.11648/j.mcs.20160101.12

    Copy | Download

    ACS Style

    Dianyu Jiang. A Matrix Representation of an n-Person 0-1 Game and Its 0-1 Tail Algorithm to Find (Strictly) Pure Nash Equilibria. Math. Comput. Sci. 2016, 1(1), 5-9. doi: 10.11648/j.mcs.20160101.12

    Copy | Download

    AMA Style

    Dianyu Jiang. A Matrix Representation of an n-Person 0-1 Game and Its 0-1 Tail Algorithm to Find (Strictly) Pure Nash Equilibria. Math Comput Sci. 2016;1(1):5-9. doi: 10.11648/j.mcs.20160101.12

    Copy | Download

  • @article{10.11648/j.mcs.20160101.12,
      author = {Dianyu Jiang},
      title = {A Matrix Representation of an n-Person 0-1 Game and Its 0-1 Tail Algorithm to Find (Strictly) Pure Nash Equilibria},
      journal = {Mathematics and Computer Science},
      volume = {1},
      number = {1},
      pages = {5-9},
      doi = {10.11648/j.mcs.20160101.12},
      url = {https://doi.org/10.11648/j.mcs.20160101.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20160101.12},
      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.},
     year = {2016}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - A Matrix Representation of an n-Person 0-1 Game and Its 0-1 Tail Algorithm to Find (Strictly) Pure Nash Equilibria
    AU  - Dianyu Jiang
    Y1  - 2016/05/09
    PY  - 2016
    N1  - https://doi.org/10.11648/j.mcs.20160101.12
    DO  - 10.11648/j.mcs.20160101.12
    T2  - Mathematics and Computer Science
    JF  - Mathematics and Computer Science
    JO  - Mathematics and Computer Science
    SP  - 5
    EP  - 9
    PB  - Science Publishing Group
    SN  - 2575-6028
    UR  - https://doi.org/10.11648/j.mcs.20160101.12
    AB  - 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.
    VL  - 1
    IS  - 1
    ER  - 

    Copy | Download

Author Information
  • Institution of Game Theory and Its Application, Huaihai Institute of Technology, Lianyungang, China

  • Sections