Personal AI agents now persist: they hold accounts, mailboxes, long-term memory, and open-ended task streams, yet the dominant way to improve them remains capability-side: prompt engineering, larger models, longer thinking, and retrieval. We argue that long-lived agents are missing an incentive layer. We formalize an incentive not as text in a prompt but as a runtime contract over the agent's operating point (model tier, test-time compute, memory budget, tool authority, task priority, verification, and compensation) that the agent's policy must causally consume. We develop a principal-agent model with hidden effort, a contractible operating point, and costly verification. We derive (i) a non-consumption invariance principle separating genuine incentives from prompt-level persuasion, (ii) a persistence-as-discount theorem making identity continuity a precondition for sustained effort, (iii) an incentive-capability exchange-rate frontier yielding a per-task routing rule, and (iv) a Goodhart bound for multi-channel verification, plus a three-channel decomposition of mechanism gains (allocation, verification, continuation). A 240-run real-LLM experiment with two models and 60 verifiable tasks shows that prompt-level incentive framing has no detectable effect (p = 0.62), whereas runtime allocation raises success on the hardest task family from 0.60 to 1.00 (p = 0.008) at 4.8x price-weighted cost; the exchange-rate theorem predicts the break-even baseline at 0.21. A 20-seed, 3,000-task simulation shows resource ROI rising from 7.09 to 16.67 and gaming falling from 0.333 to 0.115. Code, simulator, and all results are released; live deployment remains future work.

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