Competition Model of Firms in Duopoly Market Based on Differential Game and with Delayed Control Variables

The firms in duopoly markets adjust their behavior under strategic interactions to attain more market share and try to compete by different policies. In this study, we used non-delayed and delayed forms of differential game model to investigate competition between firms. Regarding quality as one of the state variables and related control variables of two firms, we have compared the results of two models and have discussed about the results of delayed form. When the delay, which is an unfavorable phenomenon, happens, the firms must behave corresponding to the equilibrium relations derived from the delayed differential game model. Effort of each firm to improve its product quality is influenced by either its delay or its competitor’s delay. The firm having less delay is able to achieve higher quality by means of less effort.