A Bertrand Duopoly Game with Long-Memory Effects

Table 1

Recent studies on dynamical duopoly games with integer-order difference equations.

Study	Game type	Decision variables	Characteristics	Reference
Ueda; Tu and Wang	Cournot game	Quantity	Bounded rationality	[1, 2]
Hsu, et al.	Cournot game	Quantity	Technology licensing	[3]
Al-khedhairi	Cournot game	Quantity	Differentiated players	[4]
Fanti et al.; Gori and Sodini; Ahmed et al.	Bertrand game	Price	Product differentiation	[8, 12, 14]
Askar and Al-khedhairi	Bertrand game	Price	Limited information	[9]
Ma and Lou	Bertrand game	Price	Integer delay	[11]
Tu et al.	Bertrand game	Price	R&D	[13]
Yang, et al.	Stackelberg game	Quantity	Bounded rationality	[15]
Peng and Lu	Stackelberg game	Quantity	Bounded rationality	[16]
Shi; Le and Sheng	Stackelberg game	Quantity	Bounded rationality	[17]
Ma et al.	Mixed game	Price, quantity	Heterogeneity	[19]
Wu	Differential game	price	Technology licensing	[20]