Influence of memory effects on quantum Stackelberg duopoly game under amplitude damping channel

doi:10.1088/1674-1056/ae29ff

Abstract We study the influence of memory effects on the quantum Stackelberg duopoly game through an amplitude-damping channel where successive uses of the channels are correlated. It is shown that the memory effects can drastically change the Nash equilibrium and the payoffs of the two firms. As the degree of channel memory increases, there exists a Nash equilibrium for the entire range of the entanglement parameter. Similarly, the presence of memory ensures the existence of the Nash equilibrium for the whole range of the decoherence parameter both for entangled and unentangled initial states. Moreover, quantum memory leads to a ‘critical point’ of the damping parameter, at which both firms are equally benefited. With the maximum-memory effect, the position of the ‘critical point’ moves to the place of fully decohered.

Keywords: Stackelberg duopoly game memory effects payoff amplitude-damping channel

Received: 08 October 2025
Revised: 10 November 2025
Accepted manuscript online: 09 December 2025

PACS:	02.50.Le	(Decision theory and game theory)
	03.67.-a	(Quantum information)
	05.30.-d	(Quantum statistical mechanics)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. U2031135).

Corresponding Authors: Xiang-Ping Liao
E-mail: liaoxp1@126.com

Cite this article:

Xiang-Ping Liao(廖湘萍) and Xin-Yi Wang(王馨仪) Influence of memory effects on quantum Stackelberg duopoly game under amplitude damping channel 2026 Chin. Phys. B 35 080203

[1] Myerson R B 1991 Game Theory: Analysis of Conflict (Boston: Havard University Press)
[2] Flitney A P and Abbott D 2005 J. Phys. A 38 449
[3] Chen L K, Ang H, Kiang D, Kwek L C and Lo C F 2003 Phys. Lett. A 316 317
[4] Chen J L, Kwek L C and Oh C H 2002 Phys. Rev. A 65 052320
[5] Khan S, Ramzan M and Khan M K 2010 Int. J. Theor. Phys. 49 31
[6] Cao S, Fang M F and Zheng X J 2007 Chin. Phys. 16 915
[7] Zhu X and Kuang L M 2008 Commun. Theor. Phys. 49 111
[8] Zhu, X and Kuang L M 2007 J. Phys. A: Math. Theor. 40 7729
[9] Macchiavello C and Palma G M 2002 Phys. Rev. A 65 050301
[10] Yeo Y and Skeen A 2003 Phys. Rev. A 67 064301
[11] Mazhar Ali 2024 Chin. Phys. B 33 020307
[12] Nawaz A and Toor A H 2006 J. Phys. A: Math. Gen. 39 9321
[13] Ramzan M, Nawaz A, Toor A H and Khan M H 2008 J. Phys. A: Math. Theor. 41 5
[14] Ramzan M and Khan M K 2013 Fluctuation and Noise Letters 12 1350025
[15] Ramzan M and Khan M K 2008 J. Phys. A: Math. Theor. 41 435302
[16] Khan S, Ramzan M and Khan M K 2010 J. Phys. A: Math. Theor. 43 375301
[17] Lo C F and Kiang D 2003 Phys. Lett. A 318 333
[18] Bierman H S and Fernandez L 1998 Game Theory with Economic Applications (MA: Addison–Wesley, Reading)
[19] Gravelle H and Rees R 1992 Microeconomics 2nd. edn. (New York: Longman Harlow)
[20] Rasmusen E 1994 Games and Information: An Introduction to Game Theory 2nd. edn. (Oxford: Blackwell Publishers)
[21] ZhangWY 2004 Game Theory and Information Economics (Shanghai: Shanghai People’s Press)
[22] Gibbons R 1992 Game theory for Applied Economists (Princeton: Princeton University Press)
[23] Iqbal A and Toor A H 2002 Phys. Rev. A 65 052328
[24] Lo C F and Kiang D 2005 Phys. Lett. A 346 65
[25] Wang X and Hu C Z 2012 Chin. Phys. Lett. 29 120303
[26] Marinatto L and Weber T 2000 Phys. Lett. A 272 291
[27] Kameshwari A V S and Balakrishnan S 2021 Quantum Inf. Process. 20 337
[28] Lian S and Feng X b 2021 Phys. Lett. A 385 126956
[29] Ramón A S and Samuel M G 2020 Physica A: Statistical Mechanics and its Applications 553 124271
[30] Khan S and Khan M K 2011 Chin. Phys. Lett. 28 070202
[31] Liao X P, Pan C N, Rong M S and Fang M F 2019 Quantum Inf. Process. 18 91

[1]	Analysis of anomalous transport with temporal fractional transport equations in a bounded domain Kaibang Wu(吴凯邦), Jiayan Liu(刘嘉言), Shijie Liu(刘仕洁), Feng Wang(王丰), Lai Wei(魏来), Qibin Luan(栾其斌), and Zheng-Xiong Wang(王正汹). Chin. Phys. B, 2023, 32(11): 110502.
[2]	Nonlocal advantage of quantum coherence in a dephasing channel with memory Ming-Liang Hu(胡明亮), Yu-Han Zhang(张宇晗), and Heng Fan(范桁). Chin. Phys. B, 2021, 30(3): 030308.
[3]	Payoff-based accumulative effect promotes cooperation in spatial prisoner's dilemma Liu Yong-Kui(刘永奎), Li Zhi(李~~智), Chen Xiao-Jie(陈小杰), and Wang Long(王~~龙). Chin. Phys. B, 2010, 19(9): 090203.
[4]	Effects of fractal gating of potassium channels on neuronal behaviours Zhao De-Jiang(赵德江), Zeng Shang-You(曾上游), and Zhang Zheng-Zhen(张争珍). Chin. Phys. B, 2010, 19(10): 108701.
[5]	Entanglement-enhanced classical communication through an amplitude-damping channel Hou Li-Zhen(侯丽珍) and Fang Mao-Fa(方卯发). Chin. Phys. B, 2007, 16(8): 2188-2193.
[6]	The Holevo capacity of a generalized amplitude-damping channel Hou Li-Zhen(侯丽珍) and Fang Mao-Fa(方卯发). Chin. Phys. B, 2007, 16(7): 1843-1847.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Influence of memory effects on quantum Stackelberg duopoly game under amplitude damping channel

Cite this article:

Online attention