Market share dynamics in a duopoly model with word-of-mouth communication

•Dynamic price competition where consumers exchange information via word-of-mouth communication.•Markov perfect equilibria where dynamics is generated not by external shocks, but via mixed strategies.•Different classes of dynamics obtained: persistence of dominance as well as tendency toward equal market shares.

We analyze dynamic price competition in a homogeneous goods duopoly, where consumers exchange information via word-of-mouth communication. A fraction of consumers, who do not learn any new information, remain locked-in at their previous supplier in each period. We analyze Markov perfect equilibria in which firms use mixed pricing strategies. Market share dynamics are driven by the endogenous price dispersion. Depending on the parameters, we obtain different 'classes' of dynamics. When firms are impatient, there is a tendency towards equal market shares. When firms are patient, there are extended intervals of market dominance, interrupted by sudden changes in the leadership position.