Nonlinear dynamics of continuous-variable quantum games with bounded rationality

Yang, Zhe; Gong, Qingbin

doi:10.1007/s11128-018-2079-3

Cited by 14 publications

(5 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since the game problem is studied from the perspective of evolutionary dynamics, the information is usually incomplete, and the game participants need to collect more information by continuously learning to adjust their strategies and gradually reach the quantized NE. In recent years, there have been a number of studies conducted on the nonlinear dynamics of quantum duopoly games under discrete-time conditions [22][23][24][25][26][27][28][29]. Firstly, the nonlinear dynamics of quantum Cournot games with homogeneous and heterogeneous expectations are examined [22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, there have been a number of studies conducted on the nonlinear dynamics of quantum duopoly games under discrete-time conditions [22][23][24][25][26][27][28][29]. Firstly, the nonlinear dynamics of quantum Cournot games with homogeneous and heterogeneous expectations are examined [22][23][24][25]. Subsequently, researchers delve into the complex dynamics of the quantum version of the Stackelberg game, featuring different cost functions and heterogeneous expectations [26,28].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Complex dynamics and chaos control of a quantum Stackelberg game with heterogeneous players

Chen

2024

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

In this research article, we explore the complex dynamics of a quantum Stackelberg game and its chaos control involving players with heterogeneous expectations. We utilize the Iqbal & Toor scheme to quantize the classical Stackelberg game and observe that the first mover advantage is diminished in the quantum version of the game. By examining the game from an evolutionary perspective, where the leader firm employs bounded rational expectations and the follower firm adopts adaptive expectations, we discover that the quantum Stackelberg game exhibits complex behaviors, such as cyclic and chaotic states. The local stability of the quantum game depends on the initial state of the game. Additionally, the occurrence of chaos is delayed in the quantum game. To further investigate, we implement the time-delayed feedback method to control the chaos in the quantum game and demonstrate that the techniques used for controlling the classical game are still effective in the quantum game.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Complex dynamics and chaos control of a quantum Stackelberg game with heterogeneous players

Chen

2024

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…Later, Li et al [6] provided a new quantum scheme for games with continuous-variable strategies. Note that the quantum scheme of [6] is an useful method to study quantum games, and more work on quantum games were studied, see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Note that, the quantum scheme is not unique for games with continuousvariable strategies.…”

Section: Introductionmentioning

confidence: 99%

The two-turn quantum games with continuous-variable strategies

Wang

Yang

2023

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

This paper investigates the two-turn quantum games with continuous-variable strategies by adopting the Li-Du-Massar method andFrackiewicz quantum scheme. We find that the entanglement level of Li-Du-Massar quantum scheme has a negative effect on the quantum equilibrium payoffs, and the entanglement level of Frackiewicz quantum scheme has a positive effect on the quantumequilibrium payoffs. Our analysis allows us to add a new look at the quantum games.

show abstract

“…Using the methods of quantum scheme in [3,5], some quantum games were given in [7][8][9][10][11][12][13][14]. On the other hand, some dynamic quantum game models were also given in [15][16][17]. Recently, the quantum games were studied in market analysis [18,19] and special two parameter strategy spaces [20].…”

Section: Introductionmentioning

confidence: 99%

Quantum games with separated entanglements

Wang,

Yang

2023

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

In this paper, we propose quantum games with continuous-variable strategies and separated entanglements, and analyze the outcomes of quantum games with respect to entanglement levels. We find that the entanglement level of own environment has a positive role in own quantum equilibrium supply quantities, and the properties of quantum equilibrium utilities are determined by the entanglement levels of two environments. Finally, we provide some numerical evidences to explain quantum games with separated entanglements.

show abstract

Nonlinear dynamics of continuous-variable quantum games with bounded rationality

Cited by 14 publications

References 25 publications

Complex dynamics and chaos control of a quantum Stackelberg game with heterogeneous players

Complex dynamics and chaos control of a quantum Stackelberg game with heterogeneous players

The two-turn quantum games with continuous-variable strategies

Quantum games with separated entanglements

Contact Info

Product

Resources

About