Equilibrium and Pricing in Consumer Networks with Nonlinear Utilities: An Online Shape-Constrained Learning Approach
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| Format: | Preprint |
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2026
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| author | Bracale, Daniele Michailidis, George |
| author_facet | Bracale, Daniele Michailidis, George |
| contents | We study optimal monopoly pricing over consumer networks governed by general nonlinear utilities. In our 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. We first establish the existence and uniqueness of the consumer-side equilibrium under general contraction and variational conditions, explicitly accommodating asymmetric and signed network externalities. Leveraging this equilibrium characterization, we analyze targeted price discrimination within community-structured and influencer-driven markets. To this end, we introduce a generalized measure of network influence that extends classical Katz-Bonacich centrality beyond the Euclidean domain. Finally, addressing the challenge of unknown consumer utility functions, we develop a shape-constrained, tuning-parameter-free learning approach utilizing isotonic regression, for which we establish strict no-regret convergence guarantees. Supported by extensive simulations, our results seamlessly integrate equilibrium analysis and nonparametric learning into a cohesive monopoly pricing framework. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_14193 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equilibrium and Pricing in Consumer Networks with Nonlinear Utilities: An Online Shape-Constrained Learning Approach Bracale, Daniele Michailidis, George Statistics Theory We study optimal monopoly pricing over consumer networks governed by general nonlinear utilities. In our 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. We first establish the existence and uniqueness of the consumer-side equilibrium under general contraction and variational conditions, explicitly accommodating asymmetric and signed network externalities. Leveraging this equilibrium characterization, we analyze targeted price discrimination within community-structured and influencer-driven markets. To this end, we introduce a generalized measure of network influence that extends classical Katz-Bonacich centrality beyond the Euclidean domain. Finally, addressing the challenge of unknown consumer utility functions, we develop a shape-constrained, tuning-parameter-free learning approach utilizing isotonic regression, for which we establish strict no-regret convergence guarantees. Supported by extensive simulations, our results seamlessly integrate equilibrium analysis and nonparametric learning into a cohesive monopoly pricing framework. |
| title | Equilibrium and Pricing in Consumer Networks with Nonlinear Utilities: An Online Shape-Constrained Learning Approach |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2605.14193 |