Walraswap proposes common-price trading backed by external liquidity

Decentralized exchanges face a problem that is partly about prices and partly about power. When the outcome of swaps depends on transaction order, those controlling block construction can exploit their position. The November 2026 version of the Walraswap preprint by Sergio Andrés Yuhjtman explores a different organizing principle: collect orders into a batch and settle participating traders’ exchanges using one common price vector.

The distinction between mathematical construction and operating exchange matters throughout this paper. Yuhjtman presents equilibrium results with proofs, then outlines an Ethereum protocol intended to use them. He explicitly describes that protocol section as exploratory, without rigorous results, and expects modifications before implementation.

Common prices, independent pools

A common price vector assigns a relative value to every token in the batch. Internal orders trade at the exchange rates implied by those values. This removes differences in exchange rates between internal trades that could otherwise reward buying and immediately reselling within the batch.

External automated market makers, or AMMs, create a complication. These pools already have their own pricing rules and swap fees. Walraswap’s construction does not require them to adopt the batch’s prices. Instead, they execute ordinary swaps, while participating orders settle at the common internal prices.

The paper models orders as continuous functions specifying how much an agent will sell or buy at different relative prices. Admissible orders must also satisfy a monotonicity condition called weak gross substitutability. Continuous limit sell orders qualify and can closely approximate conventional limit orders allowing partial execution. The framework cannot approximate orders that prohibit partial execution, and the continuous limit buy orders described in the paper do not satisfy the required monotonicity condition.

What the theorem establishes

The central result requires a connectivity condition: the directed network formed by orders and external AMMs must provide a path between every ordered pair of tokens. Under that condition, the paper establishes the existence of positive clearing prices and external swaps that fulfill the orders’ prescribed responses while leaving a nonnegative surplus of every token.

That is a feasibility statement, not a promise that every submitted order sells its full requested quantity. An order’s response depends on the selected prices and can include partial execution or no trade.

The construction uses mathematical “virtual agents” to represent external liquidity inside the equilibrium calculation. Replacing those virtual responses with actual pool swaps produces the surplus. External pools retain their own execution rules; they are not protected by the batch’s common exchange rates.

For the selected clearing-price vector, the prescribed external swaps maximize the surplus’s value measured at those prices. This qualification is important: the result does not establish a globally best outcome across every possible price vector or a trader-by-trader welfare maximum. Nor does the proposed protocol distribute that surplus directly to traders.

The paper also establishes that, under its monotonicity assumptions, individual agents’ net trades are identical across equilibria, even when equilibrium prices differ. It formulates equilibrium computation as a convex optimization problem. Practical solver design and performance remain future work rather than demonstrated deployment capabilities.

The harder question is inclusion

Common prices alone do not prevent manipulation. As the paper explains, a solver—the entity constructing and submitting a batch—could omit orders to change the outcome profitably.

Walraswap’s proposed response is public accountability backed by governance. Holders of a proposed W token would control a solver allowlist. Solvers would commit to public strategies, disclose valid orders they receive, and run deterministic batch-building algorithms whose execution others could check against disclosed inputs.

This is an incentive-based proposal, not a proof that censorship disappears. The paper acknowledges that network latency makes honesty assessments somewhat subjective. It also expects governance power to begin concentrated and specialized solver operations to consolidate among a small number of entities.

Gas costs impose another boundary. Small partial fills can be uneconomic because execution costs do not vanish with trade size. Solvers therefore need to select viable subsets of orders, with orders specifying maximum relative gas fees.

Walraswap’s contribution is a mathematical route for combining common-price order clearing with independent AMM liquidity. Its ambition to reduce extractable value rests on an additional, unresolved institutional task: making broad inclusion and accountable batch construction work under real operating constraints.