Rough nonlocal diffusions

We consider a nonlinear Fokker-Planck equation driven by a deterministic rough path which describes the conditional probability of a McKean-Vlasov diffusion with "common" noise. To study the equation we build a self-contained framework of non-linear rough integration theory which we use to study McKean-Vlasov equations perturbed by rough paths. We construct an appropriate notion of solution of the corresponding Fokker-Planck equation and prove well-posedness.Comment: 55 pages. Corrected minor typos in version

TV Advertising, Program Quality, and Product-Market Oligopoly

We present a model of the TV-advertising market that encompasses both the product markets and the market for TV programs. We argue that the TV industry has several idiosyncratic characteristics that need to be modeled, and show that the strategic interaction in this industry differs from other industries in many respects. We find that a move from a TV monopoly to a TV duopoly may reduce both the total number of viewers and the total amount of TV advertising. A softening of price competition in each product market results in more investment in program quality, higher price per advertising slot, and more advertising. A reduction of the number of firms in each product market may have the opposite effect if the price competition in the product market is sufficiently soft initially. Finally, we find that even small asymmetries between product markets can cause large asymmetries with respect to which producers buy advertising on TV.

Business Models for Media Firms: Does Competition Matter for how they Raise Revenue?

The purpose of this article is to analyze how competitive forces may influence the way media firms like TV channels raise revenue. A media firm can either be financed by advertising revenue, by direct payment from the viewers (or the readers, if we consider newspapers), or by both. We show that the scope for raising revenues from consumer payment is constrained by other media firms offering close substitutes. This implies that the less differentiated the media firms’ content, the larger is the fraction of their revenue coming from advertising. A media firm’s scope for raising revenues from ads, on the other hand, is constrained by how many competitors it faces. We should thus expect that direct payment from the media consumers becomes more important the larger the number of competing media products.