A1381
Title: Equilibrium and pricing in consumer networks with nonlinear utilities: An online shape-constrained learning approach
Authors: Daniele Bracale - University of Michigan (United States) [presenting]
George Michailidis - University of California, Los Angeles (United States)
Abstract: Optimal monopoly pricing over consumer networks governed by general nonlinear utilities is studied. In this framework, a consumer's utility is jointly determined by an individualized price and the consumption choices of their peers, propagated through a directed and signed social graph. This formulation encapsulates a broad class of utility functions; it strictly generalizes the traditional linear-quadratic framework to include logit-type discrete choice, isoelastic, and Stone-Geary utilities under a single theoretical umbrella. The existence and uniqueness of the consumer-side equilibrium is established under general contraction and variational conditions, explicitly accommodating asymmetric and signed network externalities. Leveraging this equilibrium characterization, targeted price discrimination within community-structured and influencer-driven markets is analyzed. To this end, a generalized measure of network influence is introduced that extends classical KatzBonacich centrality beyond the Euclidean domain. Finally, addressing the challenge of unknown consumer utility functions, a shape-constrained, tuning-parameter-free learning approach utilizing isotonic regression is developed, for which strict no-regret convergence guarantees are established. Supported by extensive simulations, the results seamlessly integrate equilibrium analysis and nonparametric learning into a cohesive monopoly pricing framework.
