<p>This paper examines a dynamic Bertrand duopoly game with differentiated products. It is assumed that firms are boundedly rational and have linear cost functions, while consumers possess an underlying CES utility function. For general parameters, we prove the existence and uniqueness of the Bertrand-Nash equilibrium. Regarding the stability of the model, we first discuss the case of firms with homogeneous marginal costs and establish the parameter conditions for the local stability of the Bertrand–Nash equilibrium. In the scenario of heterogeneous marginal costs, we mainly focus on two distinct degrees of product substitutability and use symbolic computation methods to derive the stability conditions. Most insightfully, it is found that increasing the product substitutability or decreasing the product differentiation may destabilize the Bertrand game, contrary to the Cournot game’s relevant results. In the case of homogeneous marginal costs, we also deduce that a lower degree of product differentiation leads to lower commodity prices, higher market supply, lower firm profits, and lower social welfare. Furthermore, complex dynamics such as quasi-periodic orbits and chaos are discovered through numerical simulations.</p>