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This research proposes a novel matching algorithm that uses spectral projection to solve multi-dimensional agent-object problems in O(N log N) time, achieving optimal Nash Social Welfare guarantees. While the study includes an agentic AI shopping application as a diagnostic test case, the core contribution lies in the theoretical advancement of game-theoretic mechanisms and machine learning optimization rather than consumer-facing AI products or policy.
Multi-Dimensional Matching
arXiv:2609.29958v1 Announce Type: cross Abstract: We study a matching mechanism where agents and objects are described by features rather than complete rankings. A single spectral projection reduces the problem to a one-dimensional sort, computable in O(N log N) time. We prove that on descaled features and preferences, our algorithm obtains the exact Nash Social Welfare (NSW) optimum within the projected space, with an unconditional utilitarian-welfare guarantee and a conditional NSW guarantee. The proposed mechanism is stable against exogenous noise but not strategy-proof; we provide an explicit profitable misreport. On an agentic AI shopping application, the diagnostics correctly anticipate both a success and a failure case. A 100-instance robustness study confirms the findings.
Abstract:We study a matching mechanism where agents and objects are described by features rather than complete rankings. A single spectral projection reduces the problem to a one-dimensional sort, computable in O(N log N) time. We prove that on descaled features and preferences, our algorithm obtains the exact Nash Social Welfare (NSW) optimum within the projected space, with an unconditional utilitarian-welfare guarantee and a conditional NSW guarantee. The proposed mechanism is stable against exogenous noise but not strategy-proof; we provide an explicit profitable misreport. On an agentic AI shopping application, the diagnostics correctly anticipate both a success and a failure case. A 100-instance robustness study confirms the findings.
Econometrics (econ.EM); Computer Science and Game Theory (cs.GT); Machine Learning (cs.LG); Multiagent Systems (cs.MA); Theoretical Economics (econ.TH)
arXiv:2609.29958 [econ.EM]
(or arXiv:2609.29958v1 [econ.EM] for this version)
https://doi.org/10.48550/arXiv.2609.29958 arXiv-issued DOI via DataCite (pending registration)
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