The Joint Clearing Bargain: How a Two-Sided Market Prices Itself

A market with no external price must referee its own trade-off between the capital that funds it and theorder flow it executes. The Joint Clearing Bargain (JCB) is a per-period optimization in which the priceand the fee are both discovered inside the clearing — no oracle, no bonding curve, no posted scheduleanywhere in the loop. Three things here are new. The objective: a scoring surface z = m^p · (1 − r^2 )^q ,pinned by boundary conditions with nothing fitted, that treats the two sides as complements under abalanced mix and substitutes under a lopsided one — a regime transition no fixed-elasticity aggregatorcan carry. The parameter: the clearing bond p, the surface’s returns to scale, is not chosen by the operatorbut measured, by a non-circular estimator whose iteration lands on a fixed point the market itself operatesat and reveals. The finding: three synthetic markets that share nothing but the mechanism return the samefixed point — p ≈ 0.60 with the fee as the only instrument, p ≈ 0.76 once the price control is switchedon — an invariant of the clearing rule, not of the assets it clears. Run against the same executed flow, aconstant-product market maker ties up roughly eighteen times the capital and pays its providers about ahundredth of the return per dollar.