Mathematical modeling and numerical analysis of blockchain decision systems by a dynamic game method

Xiaojing Li; Tianxing Liu; Feng Gu; Xiaojing Li; Tianxing Liu; Feng Gu

doi:10.3934/era.2025218

Electronic Research Archive

2025, Volume 33, Issue 8: 4837-4856. doi: 10.3934/era.2025218

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Mathematical modeling and numerical analysis of blockchain decision systems by a dynamic game method

1.
School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China
2.
School of Business, Sichuan Normal University, Chengdu, Sichuan 610101, China
3.
Stanford Online High School, Redwood City, CA 94063, USA
4.
Department of Computer Science, College of Staten Island, CUNY, Staten Island, NY 10314, USA

Received: 20 July 2025 Revised: 11 August 2025 Accepted: 13 August 2025 Published: 20 August 2025

In this study, we innovatively applied dynamic game theory to analyze blockchain adoption decisions in competitive environments. By constructing a multi-stage dynamic game model and solving for optimal strategies through backward induction, we overcame the limitations of the traditional static game analysis. Combining the mathematical modeling with numerical simulations, we identified a critical threshold effect of the competition intensity on the blockchain adoption equilibrium. Specifically, when the competition intensity fell below the threshold, blockchain adoptions emerged as the dominant strategy. Beyond this threshold, the equilibrium shifted to a mixed-strategy outcome. Furthermore, we developed a dynamic response mechanism that linked traceability preferences to profit functions. Our model provides a theoretical framework for analyzing blockchain adoptions in competitive settings, while the numerical results offer actionable insights for optimizing the blockchain system design.
- blockchain,
- dynamic game,
- mathematical modeling,
- numerical analysis
Citation: Xiaojing Li, Tianxing Liu, Feng Gu. Mathematical modeling and numerical analysis of blockchain decision systems by a dynamic game method[J]. Electronic Research Archive, 2025, 33(8): 4837-4856. doi: 10.3934/era.2025218

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Abstract

In this study, we innovatively applied dynamic game theory to analyze blockchain adoption decisions in competitive environments. By constructing a multi-stage dynamic game model and solving for optimal strategies through backward induction, we overcame the limitations of the traditional static game analysis. Combining the mathematical modeling with numerical simulations, we identified a critical threshold effect of the competition intensity on the blockchain adoption equilibrium. Specifically, when the competition intensity fell below the threshold, blockchain adoptions emerged as the dominant strategy. Beyond this threshold, the equilibrium shifted to a mixed-strategy outcome. Furthermore, we developed a dynamic response mechanism that linked traceability preferences to profit functions. Our model provides a theoretical framework for analyzing blockchain adoptions in competitive settings, while the numerical results offer actionable insights for optimizing the blockchain system design.

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