Chinese chess competition strategy analysis based on the zero-sum game

Research Article
Open access

Chinese chess competition strategy analysis based on the zero-sum game

Kaiqi Zhang 1*
  • 1 Sichuan Agriculture University    
  • *corresponding author Kaiqi.Zhang@calhoun.edu
Published on 17 November 2023 | https://doi.org/10.54254/2753-8818/12/20230427
TNS Vol.12
ISSN (Print): 2753-8826
ISSN (Online): 2753-8818
ISBN (Print): 978-1-83558-135-3
ISBN (Online): 978-1-83558-136-0

Abstract

As a desktop game with a long history, Chinese chess has been widely circulated. In recent years, Chinese chess championships have become increasingly popular. During the competition, in addition to the individual abilities of the participants, the use of different strategies in the competition also become another major factor affecting the outcome of the competition. Based on the fixed ability values of the contestants, this research focuses on discussing the selection of strategies. This paper will adopt points-based match rules in common competitions and quantify the player's ability values for making a data analysis about nine different strategies. Due to the use of a point system in the competition, this research could use zero-sum game for analysis. According to zero-sum game and Nash equilibrium, the payoff matrix could be obtained. Furthermore, a precise linear program model is built. After the calculation, this research presents a result about which strategies should be used in the competition and provide an analytical explanation.

Keywords:

Chinese chess competition, zero-sum game, linear programming, “Choking” phenomenon

Zhang,K. (2023). Chinese chess competition strategy analysis based on the zero-sum game. Theoretical and Natural Science,12,32-37.
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References

[1]. Fox W P 2010 Teaching the applications of Optimization in game theory's zero-sum and non-zero sum games. International Journal of Data Analysis Techniques & Strategies 2(3), 258-284.

[2]. Matouek J, Grtner B 2007 Understanding and Using Linear Programming. Springer Berlin Heidelberg.

[3]. Dantzig G B 2023 A proof of the equivalence of the programming problem and the game problem. Activity Analysis of Production & Allocation.

[4]. Patterson, Mike C 1990 A Linear programming model for solving complex 2-person Zero-sum games. Studies in Economics & Finance 13(2), 20-31.

[5]. Wu Z, Dang C, Karimi H R, et al 2014 A Mixed 0-1 Linear Programming Approach to the Computation of All Pure-Strategy Nash Equilibria of a Finite n-Person Game in Normal Form. Mathematical Problems in Engineering (5), 1-8.

[6]. Ca H, Ae R 2004 The Nash equilibrium: A perspective. Proceedings of the National Academy of Sciences 101(12), 3999-4002.

[7]. Daskalakis C, Goldberg P W, Papadimitriou C H 2006 The complexity of computing a Nash equilibrium. Thirty-eighth Acm Symposium on Theory of Computing. 195-259.

[8]. Satoh A, Tanaka Y 2020 Sion's minimax theorem and Nash equilibrium of symmetric three-players zero-sum game. International Journal of Mathematics in Operational Research 16.

[9]. Yang S 2021 The appearance and causes of the "Choking" phenomenon in chess games. Sports Vision (19), 22-23.

[10]. Hill D M, Hanton S, Matthews N 2010 Choking in sport: a review. International Review of Sport & Exercise Psychology 3(1), 24-39.

Cite this article

Zhang,K. (2023). Chinese chess competition strategy analysis based on the zero-sum game. Theoretical and Natural Science,12,32-37.

Data availability

The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

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About volume

Volume title: Proceedings of the 2023 International Conference on Mathematical Physics and Computational Simulation

ISBN：978-1-83558-135-3(Print) / 978-1-83558-136-0(Online)
Editor：Roman Bauer
Conference website: https://www.confmpcs.org/
Conference date: 12 August 2023
Series: Theoretical and Natural Science
Volume number: Vol.12
ISSN：2753-8818(Print) / 2753-8826(Online)

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References

[1]. Fox W P 2010 Teaching the applications of Optimization in game theory's zero-sum and non-zero sum games. International Journal of Data Analysis Techniques & Strategies 2(3), 258-284.

[2]. Matouek J, Grtner B 2007 Understanding and Using Linear Programming. Springer Berlin Heidelberg.

[3]. Dantzig G B 2023 A proof of the equivalence of the programming problem and the game problem. Activity Analysis of Production & Allocation.

[4]. Patterson, Mike C 1990 A Linear programming model for solving complex 2-person Zero-sum games. Studies in Economics & Finance 13(2), 20-31.

[5]. Wu Z, Dang C, Karimi H R, et al 2014 A Mixed 0-1 Linear Programming Approach to the Computation of All Pure-Strategy Nash Equilibria of a Finite n-Person Game in Normal Form. Mathematical Problems in Engineering (5), 1-8.

[6]. Ca H, Ae R 2004 The Nash equilibrium: A perspective. Proceedings of the National Academy of Sciences 101(12), 3999-4002.

[7]. Daskalakis C, Goldberg P W, Papadimitriou C H 2006 The complexity of computing a Nash equilibrium. Thirty-eighth Acm Symposium on Theory of Computing. 195-259.

[8]. Satoh A, Tanaka Y 2020 Sion's minimax theorem and Nash equilibrium of symmetric three-players zero-sum game. International Journal of Mathematics in Operational Research 16.

[9]. Yang S 2021 The appearance and causes of the "Choking" phenomenon in chess games. Sports Vision (19), 22-23.

[10]. Hill D M, Hanton S, Matthews N 2010 Choking in sport: a review. International Review of Sport & Exercise Psychology 3(1), 24-39.

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