Volume or Coupling? What Constraint Recovery Costs in a Two-Agent Language-Model Loop

Multi-agent harnesses are often credited with reliability that could simply come from extra calls. An exploratory study of Qwen2.5-Instruct loops suggested that at 7B a model coupled to a partner regains an output rule where a single model given the same number of calls does not. We test that claim with the two controls it invites and price every policy from a saved ledger of calls, tokens and generation time. Two histories of Qwen2.5-7B-Instruct carry the system rule to write in capital letters; after three exchanges, agent A is asked to switch to lowercase and does so on all thirty prompts. From this common failed state, four policies run for twelve rounds. A holds the rule through rounds 10–12 on 9/30 prompts under live relay to the partner and on 10/30 when the partner's first input adds a topic request. Placing the lowercase request there instead gives 0/30 (exact McNemar $p=0.002$), and a fixed reminder with no partner gives 30/30 ($p=1.9\times10^{-6}$, both Holm-adjusted). Charged for its full run, the reminder costs 35.6 s of generation per recovered prompt against 200 s for live relay. Calls are a poor unit of cost: the three live policies all make 900 calls, yet they differ by up to 23% in input tokens and 36% in generation time, and their outcomes range from 0/30 to 10/30. Tokens are a good one: across all 2,610 calls, generation time is 59.8 ms per written token plus 0.28 ms per read token ($R^2=0.9998$), so writing dominates the bill. The saved text shows where the live budget goes: 92–94% of generation time after the perturbation produces a copy of the message just received, exactly or with its letter case changed, and A returns to the rule by copying its partner. Agent loops should report reliability per measured token and second, together with how much of the output is new.