Price discrimination of buyers with identical preferences and collusion in a model of advertising

A model of advertising and price distributions is investigated whereby each seller can contact different buyers, whose preferences are identical, with different probabilities. The model features a continuum of equilibria parametrized by the ratio of the buyers contacted by one seller—differing across “market segments”—and by the other sellers. In general, the sellers practice price discrimination across segments. More asymmetric equilibria correspond to higher volumes of transactions and higher expected transaction prices. This results in a lower expected utility for the buyers and higher expected profits; thus, identifying areas of influence can help the sellers to support collusion.