Delayed dynamics in heterogeneous competition with product differentiation

Heterogeneous duopolies with product differentiation and isoelastic price functions are examined, in which one firm is quantity setter and the other is price setter. The reaction functions and the Cournot–Bertrand (CB) equilibrium are first determined. It is shown that the best response dynamics with continuous time scales and without time delays, is always locally asymptotically stable. This stability can be, however, lost in the presence of time delays. Both fixed and continuously distributed time delays are examined, stability conditions derived and the stability regions determined and illustrated. The results are compared to Cournot–Cournot (CC) and Bertrand–Bertrand (BB) dynamics. It turns out that continuously distributed lags have a smaller destabilizing effect on the equilibria than fixed lags, and both homogeneous (CC and BB) competitions are more stable than the heterogeneous competitions.