{"paper":{"title":"Equilibrium and Pricing in Consumer Networks with Nonlinear Utilities: An Online Shape-Constrained Learning Approach","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Consumer networks with nonlinear utilities admit a unique equilibrium that enables targeted monopoly pricing and online recovery of unknown demand functions.","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Daniele Bracale, George Michailidis","submitted_at":"2026-05-13T23:19:05Z","abstract_excerpt":"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"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish the existence and uniqueness of the consumer-side equilibrium under general contraction and variational conditions, explicitly accommodating asymmetric and signed network externalities... we establish strict no-regret convergence guarantees.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Consumer utilities satisfy contraction and variational conditions that guarantee a unique equilibrium; the abstract provides no explicit verification that these hold for the listed nonlinear families beyond the linear-quadratic case.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The paper establishes equilibrium existence and uniqueness for nonlinear utility consumer networks under contraction conditions and proposes a shape-constrained isotonic regression approach with strict no-regret convergence for learning utilities in targeted monopoly pricing.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Consumer networks with nonlinear utilities admit a unique equilibrium that enables targeted monopoly pricing and online recovery of unknown demand functions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c22449d931430d70287bc587cfcfb7b455def0e4a0744847328fdbdd3c75864e"},"source":{"id":"2605.14193","kind":"arxiv","version":1},"verdict":{"id":"c34e9571-d773-4889-b5d4-72f880b264c1","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:41:43.064906Z","strongest_claim":"We establish the existence and uniqueness of the consumer-side equilibrium under general contraction and variational conditions, explicitly accommodating asymmetric and signed network externalities... we establish strict no-regret convergence guarantees.","one_line_summary":"The paper establishes equilibrium existence and uniqueness for nonlinear utility consumer networks under contraction conditions and proposes a shape-constrained isotonic regression approach with strict no-regret convergence for learning utilities in targeted monopoly pricing.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Consumer utilities satisfy contraction and variational conditions that guarantee a unique equilibrium; the abstract provides no explicit verification that these hold for the listed nonlinear families beyond the linear-quadratic case.","pith_extraction_headline":"Consumer networks with nonlinear utilities admit a unique equilibrium that enables targeted monopoly pricing and online recovery of unknown demand functions."},"references":{"count":136,"sample":[{"doi":"","year":1985,"title":"Journal of econometrics , volume=","work_id":"c486f5d0-5a19-48d1-948b-ec25e5ca64ef","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1975,"title":"Journal of econometrics , volume=","work_id":"12ebbd06-3c97-4910-b93b-1a395cdca14d","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1983,"title":"Journal of labor economics , volume=","work_id":"84c9ca82-f752-4273-a998-857ff5924724","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"International Conference on Artificial Intelligence and Statistics , pages=","work_id":"a29ca979-8a92-4694-8e75-f47488e9a02a","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2003,"title":"44th Annual IEEE Symposium on Foundations of Computer Science, 2003","work_id":"8124cb94-8d93-4219-9876-9ade0072994e","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":136,"snapshot_sha256":"acc1babb0e5ecc3c23baa9fc1d1209485de22d7f5e0213b21ea0457073c6e86e","internal_anchors":2},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}