Outflow Dynamics in Modeling Oligopoly Markets: The Case of the Mobile Telecommunications Market in Poland

In this paper we introduce two models of opinion dynamics in oligopoly markets and apply them to a situation, where a new entrant challenges two incumbents of the same size. The models differ in the way the two forces influencing consumer choice -- (local) social interactions and (global) advertising -- interact. We study the general behavior of the models using the Mean Field Approach and Monte Carlo simulations and calibrate the models to data from the Polish telecommunications market. For one of the models criticality is observed -- below a certain critical level of advertising the market approaches a lock-in situation, where one market leader dominates the market and all other brands disappear. Interestingly, for both models the best fits to real data are obtained for conformity level $p \in (0.3,0.4)$. This agrees very well with the conformity level found by Solomon Asch in his famous social experiment.