Higher order lags in continuous time price-adjusting oligopoly models

We consider price-adjusting oligopoly models involving Bertrand or adaptive expectations concerning the rivals' prices. Traditionally, one specifies these models with first order exponential adjustment lags. We introduce specific higher order exponential lags in both models, which provides a more flexible and richer dynamic specification. We show that in both cases the model with higher order lags is stable if and only if the model with first order lags is stable.