Dynamical Cournot game with bounded rationality and time delay for marginal profit

Dynamics of a Duopoly Game with Two Different Delay Structures

“…Onetime delay, two-time delay, continuously distributed time delay, and geometric delay are systematically reviewed and studied in [20][21][22], which offer results on existence, stability, and local bifurcations of the equilibrium points. Besides, the work in [23][24][25][26][27][28] studied the dynamical Cournot game with delayed bounded rationality and found that time delay can increase the system stability and delay the occurrence of complex behaviors. Ma and Si [29] also confirmed that the stability of the system depends on the delay and weight.…”

“…In [23-25, 27, 28] time delay is done for the output variable so that decision makers' expectations are based on the delayed data of their outputs, which implicitly means that any player must know each opponent's output in the previous periods. These models may not be suitable for the market with incomplete information where a decision maker has too limited knowledge to get the opponents' output data [26]. It is also pointed out [26] that any producer is able to know his own marginal profit, which is the profit of the last unit production and can be observed in its accounting.…”

“…These models may not be suitable for the market with incomplete information where a decision maker has too limited knowledge to get the opponents' output data [26]. It is also pointed out [26] that any producer is able to know his own marginal profit, which is the profit of the last unit production and can be observed in its accounting. Then Ding et al [26] considered a case that each player makes adjustment strategy according to the delayed marginal profit, the one that averages his own previous marginal profits with different weights.…”

“…It is also pointed out [26] that any producer is able to know his own marginal profit, which is the profit of the last unit production and can be observed in its accounting. Then Ding et al [26] considered a case that each player makes adjustment strategy according to the delayed marginal profit, the one that averages his own previous marginal profits with different weights. Besides the information of marginal profit, in this work we will consider another fact that the market price history is usually a common knowledge to every player.…”

“…In this work, we reconsider the duopoly model in Ding et al [26]. But different from [26] that only considers homogeneous players and only discusses the time delay structure built for the marginal profit, this paper revises the model and assumes that in the duopoly market the two players are heterogeneous and they consider different time delay structures.…”