Mathematics and Computer Science

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

Received: 02 April 2016    Accepted: 11 April 2016    Published: 09 May 2016
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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.

DOI 10.11648/j.mcs.20160101.12
Published in Mathematics and Computer Science (Volume 1, Issue 1, May 2016)
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), 2024. 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.
Author Information
  • Institution of Game Theory and Its Application, Huaihai Institute of Technology, Lianyungang, China

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  • 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

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    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

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    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

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  • @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://download.sciencepg.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}
    }
    

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    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.
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