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

Basic facts:

• Markets are structured around a question with a binary outcome (either YES or NO)
• Traders can place a bet on either YES or NO. The bet amount is added to the corresponding bet pool for the outcome. The trader receives some shares of the final pool. The number of shares depends on the current implied probability.
• When the market is resolved, the traders who bet on the correct outcome are paid out of the total pool (YES pool + NO pool) in proportion to the amount of shares they own, minus any fees.

Probability

If $y is the amount of money in the YES pool, and $n is the amount of money in the NO pool, the instantaneous probability of the event is given as

$P(y, n) = y^2 / (y^2 + n^2)$

Betting

If a trader places a bet of $b on YES, he adds $b into the YES pool and receives s shares of the final pot if YES is the outcome:

$$ y_{new} = y_{current} + b $$

$$ s = \int_0^b \frac{1}{P(y+x,n)} dx = \int_0^b \frac{(y+x)^2+n^2}{(y+x)^2} dx

$$

The quantity $s can also be understood as the payout a risk-neutral trader who paid $b would accept for event an occurring with probability P.

Antes

Mantic Markets uses fictitious capital to initialize the betting pools. The market creator chooses an initial probability p and we allocate $200 of fake money based on their choice.

$$ p = \frac{y_{start}^2}{y_{start}^2+n_{start}^2} \; \newline s.t. \; \; y_{start}+n_{start}= 200 \newline y_{start},n_{start} \gt 0 $$

This fictitious starting capital is included in share purchase calculations but not payouts.