Agent-to-agent economies for infrastructure

What the algebra settled

The simulation is noisy in places, so we proved the parts that do not depend on a fixture. Two results came out clean, and they changed our reading of our own numbers.

The seller's loss is exact. Holding the allocation and the stopping rule fixed, switching the unit transfers precisely B(1 − q) / 2 from seller to buyer, and total surplus does not move at all. Redenominating a contract, by itself, creates nothing. It decides who holds the risk.

The delivery improvement is universal, and it comes from somewhere else. Under occupancy pricing the buyer decides when to give up while facing a marginal cost of p, the marked-up price rather than the resource's true cost r. So it quits while continuing is still worth doing. Move the option to the seller and the continuation ceiling is always weakly larger, by an argument that reduces to (B − rH)² ≥ 0.

The efficiency does not come from paying for outcomes. It comes from who is allowed to stop.

That has a sharp practical reading for anyone designing an agent-to-agent contract. A contract that pays on delivery but leaves the abandonment decision with the buyer captures the whole transfer and none of the gain.

And the uncomfortable part

Sellers are worse off under completion pricing at every hazard level we tested, by up to −$12.41. That answers the question that should have been asked first. If the unit is wrong, why has nobody changed it? Because the side that sets the terms is the side that gains from the current ones, and no argument for completion-denominated capacity is complete without saying who moves first.

Work on capacity that can be reclaimed has to be checkpointed, and how often is the oldest question in the area. The classical answer minimises expected time to finish. That is the right target for a batch system trying to get through as much work as possible.

It is the wrong target for a delegated agent. An agent with a hard budget is indifferent between finishing far under the ceiling and finishing just under it. What it wants is the largest probability of landing underneath, and that objective is sensitive to variance where the classical one is not.

The rule is simple enough to act on. Compare the ceiling to the expected cost of finishing. Above it, checkpoint more often than the textbook says. Below it, checkpoint less. The classical interval is correct at exactly one budget, the one equal to its own mean, and the direction of the error everywhere else follows from that single comparison with no extra estimation.

The size is worth noticing. In the regime where checkpoints are expensive relative to the work, the ceiling-aware interval is worth 51 pts of completion probability at a 0.80× ceiling. That is not a rounding difference. It is most of the achievable outcome.

This one is not ours We derived it, then went looking for prior art and found it. The real-time systems literature calls this objective Level of Confidence and has been maximising it over checkpoint count since at least 2011. We are publishing it anyway, for two reasons. It is directly relevant to agent-held budgets, which is a newer setting than the one it was developed for. And almost nobody implements it, including us. A fifteen-year-old method that production systems do not use is worth pointing at.

What we intend to do about it. Our cadence policy reads interrupt rate, checkpoint size, and runtime, holding lost work to a fixed share of mean time between reclaims. The cost ceiling sits at that call site unread. Adding it is a small change to one function.

We have not made it, and not out of modesty about the result. The gain above is measured against a hazard we set rather than observed, so we would be tuning against an invented number and shipping the confidence that comes with a table. The change lands when live wholesale routes give us a measured rate. Until then the fixed share is wrong in a direction we can name, which is the better default.

• Reserve prices. assumed: synthetic opportunity costs spanning a plausible range, not observed supplier economics.
• Reclaim rates. assumed: synthetic per-hour reclaim rates spanning a plausible range, scaled by hazard_mult.
• Clearing. uniform-price sealed-bid double auction, cleared at the midpoint of the marginal bid and ask, then assigned to the lowest-asking unit that fits.
• after a reclaim the job recovers onto the same unit rather than re-clearing the market; this understates the cost of the occupancy regime, so it biases against the model's own prediction.
• each side prices against the segment's typical counterparty, because neither can see its match before it exists.
• the market clears once per population rather than continuously; freed capacity is not re-offered.
• reclaim is memoryless, so a unit's hazard does not depend on how long the job has been running.
• Finding 02 sweeps 3 parameter regimes, with hazards and write costs set rather than measured. Its empirical content is internal: it evaluates a scheduling rule by simulating scheduling rules, which needs no supplier data to mean something.

Demand agents are real workload submissions profiled through the shipped profiler, and the population spans accelerator and non-accelerator capacity and durable and ephemeral work. A finding drawn only from long checkpointable training would overstate itself, since that is the case where preserving progress pays off most. Supply agents are anonymous by construction. Neither page is a measurement.

Both findings describe one asymmetry from two sides. Reclaim costs the buyer and not the seller, and an agent spending a delegated budget has nobody watching it find that out. Nodus sits on the buyer's side: route for expected cost to completion, reserve recovery money before reserving a machine, treat progress as something that must survive the instance that produced it.

Neither result is a product claim. We do not sell completion-denominated capacity, and Finding 01 says that instrument moves risk rather than creating value. What both tell us is where to spend effort: on who is allowed to stop, and on how little is thrown away when they do.

• Field note 003 is the routing objective these models are arguing with.
• Field note 006 is the cadence and manifest machinery Finding 02 is about.
• The docs are how you submit a workload against it.