A Bertrand Duopoly Game with Long-Memory Effects

Baogui Xin, Fangrui Cao, Wei Peng and Abdelalim A. Elsadany

Complexity, 2020, vol. 2020, 1-7

Abstract:

Reconsidering the Bertrand duopoly game based on the concept of long short-term memory, we construct a fractional-order Bertrand duopoly game by extending the integer-order game to its corresponding fractional-order form. We build such a Bertrand duopoly game, in which both players can make their decisions with long-memory effects. Then, we investigate its Nash equilibria, local stability, and numerical solutions. Using the bifurcation diagram, the phase portrait, time series, and the 0-1 test for chaos, we numerically validate these results and illustrate its complex phenomena, such as bifurcation and chaos.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:2924169

DOI: 10.1155/2020/2924169

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