Differential pricing with inequity aversion in social networks

We introduce and study the algorithmic problem of maximizing revenue in a network using differential pricing, where the prices offered to neighboring vertices cannot be substantially different. Our most surprising result is that the optimal pricing can be computed efficiently, even for arbitrary revenue functions. In contrast, we show that if one is allowed to introduce discontinuities (by deleting vertices) the optimization problem becomes computationally hard, and we exhibit algorithms for special classes of graphs. We also study a stochastic model, and show that a similar contrast exists there: For pricing without discontinuities the benefit of differential pricing over a single price is negligible, while for differential pricing with discontinuities the difference is substantial.