{"title":"Complex dynamics of a quantum Cournot duopoly game with two different objectives","authors":"Longfei Wei, Lu Liu, Zhenhua Bao","doi":"10.1007/s11128-024-04502-x","DOIUrl":null,"url":null,"abstract":"<div><p>In this work, a dynamic quantum Cournot duopoly game with two different objectives is proposed by applying the Li-Du-Massar quantization scheme. In this game, the first player is a (semi-) public firm adopting bounded rationality and aims to maximize the weighted sum of its own profit and social welfare, while the second player focus on the objective to maximize its own profit as a private firm with naïve expectation. The local stability conditions for the quantum Nash equilibrium of the system are analyzed. Numerical simulations are presented to display the dynamic behaviors including stability region, bifurcation and chaos diagrams, and sensitive dependence on initial conditions. The results of theoretical and numerical analysis show that a larger weight on profit or adjustment speed parameter can enhance the stability of the quantum Cournot duopoly system. Differently, a higher entanglement level will hasten the local instability of the quantum Nash equilibrium point. It is also shown that a larger quantum entanglement weakens the sensitivity to initial conditions. Moreover, the equilibrium of the system can loose stability via flip bifurcation while varying the value of the adjustment speed, and time-delayed feedback control method can be applied to stabilize the chaotic behaviors.</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Information Processing","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11128-024-04502-x","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
In this work, a dynamic quantum Cournot duopoly game with two different objectives is proposed by applying the Li-Du-Massar quantization scheme. In this game, the first player is a (semi-) public firm adopting bounded rationality and aims to maximize the weighted sum of its own profit and social welfare, while the second player focus on the objective to maximize its own profit as a private firm with naïve expectation. The local stability conditions for the quantum Nash equilibrium of the system are analyzed. Numerical simulations are presented to display the dynamic behaviors including stability region, bifurcation and chaos diagrams, and sensitive dependence on initial conditions. The results of theoretical and numerical analysis show that a larger weight on profit or adjustment speed parameter can enhance the stability of the quantum Cournot duopoly system. Differently, a higher entanglement level will hasten the local instability of the quantum Nash equilibrium point. It is also shown that a larger quantum entanglement weakens the sensitivity to initial conditions. Moreover, the equilibrium of the system can loose stability via flip bifurcation while varying the value of the adjustment speed, and time-delayed feedback control method can be applied to stabilize the chaotic behaviors.
期刊介绍:
Quantum Information Processing is a high-impact, international journal publishing cutting-edge experimental and theoretical research in all areas of Quantum Information Science. Topics of interest include quantum cryptography and communications, entanglement and discord, quantum algorithms, quantum error correction and fault tolerance, quantum computer science, quantum imaging and sensing, and experimental platforms for quantum information. Quantum Information Processing supports and inspires research by providing a comprehensive peer review process, and broadcasting high quality results in a range of formats. These include original papers, letters, broadly focused perspectives, comprehensive review articles, book reviews, and special topical issues. The journal is particularly interested in papers detailing and demonstrating quantum information protocols for cryptography, communications, computation, and sensing.