pm-AMM

In determinism, we use the pm-AMM as the core liquidity provision mechanism for prediction markets.

PM-AMM uses probability-weighted invariants based on normal distribution:

(Y - X) \times \Phi\left(\frac{Y - X}{L}\right) + L \times \phi\left(\frac{Y - X}{L}\right) - Y = 0

Symbol	Description
$Y, X$	Reserves of each outcome token in the pool
$L$	Liquidity parameter (determines market depth)
$\Phi$	Normal cumulative distribution function (probability)
$\phi$	Normal probability density function (price sensitivity)

The market price equals the probability from the normal CDF:

P_X = \Phi\left(\frac{Y - X}{L}\right)

P_Y = 1 - P_X

This page summarizes the key concepts from Paradigm’s research paper “pm-AMM: A Uniform AMM for Prediction Markets” by Ciamac Moallemi and Dan Robinson.