Nonlinear dynamics of a heterogeneous quantum Commons’ tragedy

Zhou, Die; Pi, Jinxiu; Yang, Guanghui; Ye, Hui

doi:10.1016/j.physa.2022.128231

Cited by 8 publications

(3 citation statements)

References 23 publications

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“…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%

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

Chen

2024

J. Phys. A: Math. Theor.

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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.

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Section: Introductionmentioning

confidence: 99%

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

Chen

2024

J. Phys. A: Math. Theor.

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“…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.

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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.

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“…Each type of player adjusts the production for future periods to maximise their profit using a different strategy. Our article is inspired by [32], which builds a nonlinear dynamic system of the tragedy of the commons with quantum strategies in discrete time, considering a quadratic uptake's average function and heterogeneous players. On the contrary, our model implements a lineal uptake's average function and the case of homogeneous expectations, which can be understood as if both players compete under the same conditions, involving in this case two boundedly rational players.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Quantum Common-Pool Resource Game with Homogeneous Players’ Expectations

Grau-Climent,

García-Pérez,

Alonso-Sanz

et al. 2023

Entropy

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In this work, we analyse a common-pool resource game with homogeneous players (both have boundedly rational expectations) and entanglement between players’ strategies. The quantum model with homogeneous expectations is a differential approach to the game since, to the best of our knowledge, it has hardly been considered in previous works. The game is represented using a Cournot type payoff functions, limited to the maximum capacity of the resource. The behaviour of the dynamics is studied considering how the fixed points (particularly the Nash equilibrium) and the stability of the system vary depending on the different values of the parameters involved in the model. In the analysis of this game, it is especially relevant to consider the extent to which the resource is exploited, since the output of the players is highly affected by this issue. It is studied in which cases the resource can be overexploited, adjusting the parameters of the model to avoid this scenario when it is possible. The results are obtained from an analytical point of view and also graphically using bifurcation diagrams to show the behaviour of the dynamics.

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Nonlinear dynamics of a heterogeneous quantum Commons’ tragedy

Cited by 8 publications

References 23 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

Quantum games with separated entanglements

Dynamics of a Quantum Common-Pool Resource Game with Homogeneous Players’ Expectations

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