Dynamics of a Duopoly Game with Two Different Delay Structures

Abstract EN

Two different time delay structures for the dynamical Cournot game with two heterogeneous players are considered in this paper, in which a player is assumed to make decision via his marginal profit with time delay and another is assumed to adjust strategy according to the delayed price.

The dynamics of both players output adjustments are analyzed and simulated.

The time delay for the marginal profit has more influence on the dynamical behaviors of the system while the market price delay has less effect, and an intermediate level of the delay weight for the marginal profit can expand the stability region and thus promote the system stability.

It is also shown that the system may lose stability due to either a period-doubling bifurcation or a Neimark-Sacker bifurcation.

Numerical simulations show that the chaotic behaviors can be stabilized by the time-delayed feedback control, and the two different delays play different roles on the system controllability: the delay of the marginal profit has more influence on the system control than the delay of the market price.