{"title":"Nonlinear dynamics of a quantum Cournot triopoly game with heterogeneous players","authors":"Longfei Wei, Shouli Wang, Zhenhua Bao","doi":"10.1007/s11128-025-04739-0","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, quantum game theory is applied to develop a dynamic model of the quantum Cournot triopoly game. First, we construct a nonlinear dynamic quantum Cournot triopoly game characterized by players with heterogeneous expectations. The three players are considered to be boundedly rational, naïve, and adaptive. Second, the local stability of the quantum equilibrium, the influence of quantum entanglement on stability region, and nonlinear dynamic behavior of the discrete dynamical system are analyzed. Numerical simulations are used to illustrate the stability region, bifurcation and chaos diagrams, strange attractors, and sensitive dependence on initial conditions. Finally, an appropriate control scheme is applied to stabilize the chaotic behavior at the quantum Nash equilibrium point.</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":"24 5","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2025-04-29","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/s11128-025-04739-0","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}
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Abstract
In this paper, quantum game theory is applied to develop a dynamic model of the quantum Cournot triopoly game. First, we construct a nonlinear dynamic quantum Cournot triopoly game characterized by players with heterogeneous expectations. The three players are considered to be boundedly rational, naïve, and adaptive. Second, the local stability of the quantum equilibrium, the influence of quantum entanglement on stability region, and nonlinear dynamic behavior of the discrete dynamical system are analyzed. Numerical simulations are used to illustrate the stability region, bifurcation and chaos diagrams, strange attractors, and sensitive dependence on initial conditions. Finally, an appropriate control scheme is applied to stabilize the chaotic behavior at the quantum Nash equilibrium point.
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.
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