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A fractional-order difference Cournot duopoly game with long memory

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Document pages: 19 pages

Abstract: We reconsider the Cournot duopoly problem in light of the theory for longmemory. We introduce the Caputo fractional-order difference calculus toclassical duopoly theory to propose a fractional-order discrete Cournot duopolygame model, which allows participants to make decisions while making full useof their historical information. Then we discuss Nash equilibria and localstability by using linear approximation. Finally, we detect the chaos of themodel by employing a 0-1 test algorithm.

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