A brief technical overview of Manifold Markets’ Dynamic Parimutuel (DPM) betting system

By Stephen Grugett

Note: Manifold is no longer using DPM for binary markets but is using the generalized, multi-outcome version of DPM for free-response markets.

Basic facts:

Probability

If y is the total number of outstanding shares of YES, and n is the total number of outstanding shares of NO, the instantaneous implied probability of the market is given as

$$ P(y, n) = \frac{y^2} {y^2 + n^2} $$

Betting

We introduce a cost function C which captures the total amount wagered by all traders given the current shares of YES and NO:

$$ C(y,n) = \sqrt{y^2 + n^2} $$

If a trader places a bet of $b on YES, they add $b into the YES pool and receives s shares of the final pool if YES is the outcome.

$$ pool_{Y_{new}} = pool_{Y_{current}} + b $$

$$ b = C(y+s, n) - C(y, n) $$

Antes

The market creator chooses an initial probability p and an ante amount to initialize the betting pool.

$$ p = \frac{y_{start}^2}{y_{start}^2+n_{start}^2} \; \newline s.t. \; \; \sqrt{y_{start}^2+n_{start}^2}= ante \newline y_{start},n_{start} \gt 0 $$