Effect of players’ expectations and memory in a quantum Cournot game

Juan Grau-Climent, Luis Garcia-Perez, Ramon Alonso-Sanz and Juan C. Losada

Chaos, Solitons & Fractals, 2023, vol. 175, issue P1

Abstract: The study of Game Theory is widely developed currently and has many applications in several fields such as economics, psychology, biology, etc. The use of quantum theory is a demonstrated way to improve the results comparing to the classic games due to the entanglement between the players. As well, it is known the positive effect of implementing long term memory in the stability of a dynamical system. In this context, memory is applied to the model of a quantum dynamical Cournot duopoly game considering two different cases, depending on the players’ expectations and the mechanisms they used to maximize their profits. In this work we analyse the game with homogeneous players, considering two boundedly rational players, and the game with heterogeneous expectations, where one of the players is boundedly rational and the other one is a naive player, comparing the results obtained in both cases. Firstly, we come to the conclusion that neither memory nor the type of players (heterogeneous or homogeneous) produces variations in the stable fixed points comparing to the quantum, or even, classic Cournot duopoly game and, therefore, Nash equilibrium is preserved. Secondly, it is observed that the game with homogeneous players, which is not deeply studied previously in quantum games, can improve the local stability of the system versus the game with heterogeneous players, under certain conditions. Finally, it is shown the role of memory as an effective mechanism of chaos control. This achievement is a remarkable economic advantage, since enables the system to reach the stability faster. Throughout this article, these statements are proved analytically and supported widely with several numerical simulations, using different values of the memory factor.

Keywords: Quantum game; Memory; Heterogeneous players; Homogeneous players; Local stability; Bifurcation and Chaos (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923008512

DOI: 10.1016/j.chaos.2023.113950

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