AI systems increasingly let one model choose another: an orchestrator routing a task to a sub-agent, or an agent picking a tool from a registry, by self-described ability. What happens when that self-report cannot be checked? In MATCHMARKET, a client hires one of three candidates whose true competence is hidden (2, 5, or 8 of 10), earning the competence of its hire. Candidates are themselves language models, inflating claims under an audit-and-fine incentive. Selectors rarely fall for the loudest liar, picking the inflator only 8–15% of the time. They fail by fleeing to mediocrity: 75–89% of their mistaken hires land on a safe, moderate candidate, not on the liar. A trivial yardstick makes the cost concrete: believing the highest claim earns 6.72 of a possible 8.0, and no selector we test significantly beats it. The best merely matches it, while the weakest fall significantly below (pooled 5.99, paired p = .002; random scores 5.0). A verified record recovers much of the loss, but only for selectors near chance without it, widening rather than closing cross-model gaps. Every outcome is scored arithmetically, no LLM judge. Unverified capability advertisement behaves like a market for lemons whose cost falls on the honest, capable provider.