The dynamics of a quantum Bertrand duopoly with differentiated products and heterogeneous expectations

Xinli Zhang, Deshan Sun, Sijia Ma and Shuning Zhang

Physica A: Statistical Mechanics and its Applications, 2020, vol. 557, issue C

Abstract: Based on the bounded rationality and naïve expectation, the paper sets up a dynamic model of quantum Bertrand duopoly game with differentiated products by applying quantum game theory. We analyze the effect of quantum entanglement on stability of the quantum equilibrium points and complex dynamic behaviors. The result shows that the quantum entanglement can enhance the stability of the system. The adjustment speeds of bounded rational player can lead to chaotic characteristics of the system, the quantum entanglement can control the system’s chaos. Numerical simulations demonstrate the chaotic features via bifurcation, largest Lyapunov exponent, strange attractors, fractal dimensions and sensitivity to initial conditions.

Keywords: Complex dynamics; Quantum Bertrand duopoly; Heterogeneous expectations; Differentiated products; Quantum entanglement (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:557:y:2020:i:c:s0378437120304544

DOI: 10.1016/j.physa.2020.124878

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