  In this paper, we explore a dynamic Bertrand duopoly game with differentiated
products, where firms are boundedly rational and consumers are assumed to
possess an underlying CES utility function. We mainly focus on two distinct
degrees of product substitutability. Several tools based on symbolic
computations such as the triangular decomposition method and the PCAD method
are employed in the analytical investigation of the model. The uniqueness of
the non-vanishing equilibrium is proved and rigorous conditions for the local
stability of this equilibrium are established for the first time. Most
importantly, we find that increasing the substitutability degree or decreasing
the product differentiation has an effect of destabilization for our Bertrand
model, which is in contrast with the relative conclusions for the Cournot
models. This finding could be conducive to the revelation of the essential
difference between dynamic Cournot and Bertrand oligopolies with differentiated
goods. In the special case of identical marginal costs, we derive that lower
degrees of product differentiation mean lower prices, higher supplies, lower
profits, and lower social welfare. Furthermore, complex dynamics such as
periodic orbits and chaos are reported through our numerical simulations.
