A discrete fractional-order Cournot duopoly game

Baogui Xin, Wei Peng and Yekyung Kwon

Physica A: Statistical Mechanics and its Applications, 2020, vol. 558, issue C

Abstract: This paper focuses on associating the Cournot duopoly problem with long-memory effects. First of all, we generate a discrete fractional-order Cournot duopoly game by introducing the Caputo fractional-order difference calculus to the classical duopoly theory. In the fractional-order game, participants can make their decisions by taking full advantage of their historical information. Then we discuss both Nash equilibria and local stability of the game by employing the linear approximation theory. At last, we numerically validate the main results by using bifurcation diagrams, phase portraits, the largest Lyapunov exponent, and the 0–1 test algorithms.

Keywords: Fractional difference equation; Discrete fractional-order dynamical systems; Cournot duopoly game; Bifurcation and chaos; 0–1 test for chaos (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:558:y:2020:i:c:s0378437120305185

DOI: 10.1016/j.physa.2020.124993

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