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In this paper, we explore a dynamic Bertrand duopoly game with differentiatedproducts, where firms are boundedly rational and consumers are assumed topossess an underlying CES utility function. We mainly focus on two distinctdegrees of product substitutability. Several tools based on symboliccomputations such as the triangular decomposition method and the PCAD methodare employed in the analytical investigation of the model. The uniqueness ofthe non-vanishing equilibrium is proved and rigorous conditions for the localstability of this equilibrium are established for the first time. Mostimportantly, we find that increasing the substitutability degree or decreasingthe product differentiation has an effect of destabilization for our Bertrandmodel, which is in contrast with the relative conclusions for the Cournotmodels. This finding could be conducive to the revelation of the essentialdifference between dynamic Cournot and Bertrand oligopolies with differentiatedgoods. In the special case of identical marginal costs, we derive that lowerdegrees of product differentiation mean lower prices, higher supplies, lowerprofits, and lower social welfare. Furthermore, complex dynamics such asperiodic orbits and chaos are reported through our numerical simulations.

A Bertrand duopoly game with differentiated products reconsidered