Credibility Trilemma in Polymatroidal Service Markets

2026-05-26

AI Summary

This study addresses a fundamental tension in polyhedral service markets: when platform operators act as strategic agents, it is impossible to simultaneously achieve revenue optimality, dominant-strategy incentive compatibility for agents, and operator credibility—a trilemma termed the “credibility trilemma.” The work introduces this impossibility result alongside a novel metric, the Cost of Non-Credibility (CoNC), establishing credibility as a core design constraint. Leveraging mechanism design, game theory, and graph-structural analysis, the authors derive tight Θ-bounds on CoNC across five canonical topologies and general directed acyclic graphs (DAGs), providing an O(|𝒮|) upper bound and a matching Ω(|𝒮|) lower-bound instance. The analysis further uncovers the structural role of market neutrality, proposes three topology-based resolution strategies, and empirically validates the robustness of the trilemma in edge-pricing markets.

Abstract

Mechanism-mediated service markets with polymatroidal feasibility admit efficient, dominant-strategy incentive-compatible (DSIC) allocation, but these guarantees implicitly assume truthful execution by the marketplace operator. Modelling the operator as a strategic player, we establish a credibility trilemma: for single-parameter agents on a non-modular polymatroid, no static sealed-bid mechanism is simultaneously revenue-optimal, DSIC for agents, and credible for the operator. We introduce the Cost of Non-Credibility (CoNC) as a price-of-anarchy-style welfare-loss measure and obtain tight $Θ$-bounds across five topology classes (single-edge, series, parallel, tree, series-parallel), plus a matching upper bound $O(|\mathcal{S}|)$ on general DAGs realised by an $Ω(|\mathcal{S}|)$ witness on the SP-augmented sub-family, turning the trilemma into a structural quantity. Three structurally distinct resolutions follow: public broadcast or deferred-revelation commitment, administrative domain separation under settlement separation and four side conditions, and integrator competition orthogonal to mechanism execution under disjoint actors. An instance-level grounding over the edge-pricing market of Amin et al. confirms the trilemma's robustness on a refereed external setting. The result establishes marketplace neutrality as a first-order design constraint on polymatroidal service markets rather than an implementation detail: where the operator is a strategic player, credibility trades off against revenue optimality and agent incentive compatibility along structurally characterised lines.

Problem

• credibility trilemma
• polymatroidal service markets
• dominant-strategy incentive-compatible
• revenue optimality
• strategic operator

Innovation

• credibility trilemma
• polymatroidal service markets
• Cost of Non-Credibility
• dominant-strategy incentive-compatible
• marketplace neutrality