Mean Field Game Model for an Advertising Competition in a Duopoly

In this study, we analyze an advertising competition in a duopoly. We consider two different notions of equilibrium. We model the companies in the duopoly as major players, and the consumers as minor players. In our first game model, we identify Nash Equilibrium (NE) between all the players. Next we frame the model to lead to the search for Multi-Leader-Follower Nash Equilibrium (MLF-NE). This approach is reminiscent of Stackelberg games in the sense that the major players design their advertisement policies assuming that the minor players are rational and settle in a Nash Equilibrium among themselves. This rationality assumption reduces the competition between the major players to a two-player game. After solving these two models for the notions of equilibrium, we analyze the similarities and differences of the two different sets of equilibria.