Nonlinear dynamics of a heterogeneous quantum Commons’ tragedy

Die Zhou, Jinxiu Pi, Guanghui Yang and Hui Yang

Physica A: Statistical Mechanics and its Applications, 2022, vol. 608, issue P1

Abstract: This paper first builds a nonlinear dynamic system of the Commons’ tragedy with quantum strategies in discrete time. There are two heterogeneous expectations in the game, namely, one of the two players is boundedly rational and the other is of adaptive expectation. Secondly, we obtain a sufficient and necessary condition for quantum Nash equilibria to be stable equilibria. Finally, we investigate the impacts of quantum entanglement on the stable region of systems and analyze the behaviors of complex dynamical systems. The results show that quantum Nash equilibria are stable points of nonlinear dynamics for quantum Commons’ tragedy if both quantum entanglement and quantum strategy adjustment speed satisfy certain conditions. In addition, numerical simulations discuss the features of nonlinear dynamics, such as bifurcation, the largest Lyapunov exponent, fractal dimension, strange attractor, and sensitivity to initial conditions. The numerical results show that nonlinear dynamics appear chaotic if the adjustment speed of quantum strategy or the quantum entanglement degree is larger.

Keywords: Quantum Commons’ tragedy; Heterogeneous players; Local stability analysis; Quantum entanglement (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437122007890
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:608:y:2022:i:p1:s0378437122007890

DOI: 10.1016/j.physa.2022.128231

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().