Credibility Trilemma in Polymatroidal Service Markets
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 carrying a competitive prior profile, 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 prove a per-pair lower bound scaling with the polymatroid's non-modularity gap, turning the trilemma into a quantitative diagnostic. 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. shows that the economic content carries over to a refereed external setting. Marketplace neutrality is thus 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.