Markets as Distributed Computation
We formalize a price-mediated exchange market as a distributed message-passing algorithm computing a global price vector, and prove convergence under assumptions that match the empirically observed structure of limit-order books. The theory predicts a previously unreported phase transition between two qualitatively different price-discovery regimes.
Setup
A market is a set of agents exchanging messages (orders) over a noisy channel. The market clearing price is the fixed point of a belief-propagation operator.
Main theorem
Under conditions that are satisfied whenever the order book is *not* pathologically thin, the system converges in O(log n) rounds to a price vector that is ε-close to the Walrasian equilibrium, with ε bounded by the channel noise.
Predictions
- A phase transition in price-discovery regime as a function of order-book depth.
- A quantitative formula for the latency–volatility trade-off observed in
high-frequency data.
- An explanation for the empirical failure of TWAP benchmarks in illiquid markets.