Optimal marketing decision in a duopoly: A stochastic approach

Let us consider two new perfect substitute durable products which are produced and sold in a market by two competing firms. Looking at a potential buyer, we build a stochastic rule by which she purchases the good from one of the two firms (so that she becomes an adopter). The model is considered discrete in time and space. The probability of transition from the non adopter state to the adopter one depends on an imitation mechanism (word-of-mouth) as well as on the pricing and advertising policies of the producers/sellers. It is assumed that only actual information about the market determine the evolution in the subsequent time step so that a Markov process arises. Both firms maximize their expected discounted profits by choosing optimal marketing strategies. Suitable equilibria are characterized and, because of the lack of convexity in the model, the simulated annealing algorithm is proposed to compute them.