Illustration of the market mechanism.

<p>Left: example distributions of orders received in one trading period (orange—orders to buy, blue—orders to sell). Middle: the corresponding demand and supply curves, showing the number of orders to buy above (resp. sell below) a certain price. The vertical black line marks the equilibrium trading price, i.e. the price at which demand equals supply, while the arrows show how the trading price changes for nonzero <i>θ</i>; the dashed line is the trading price for <i>θ</i> = 0.3. Right: example distributions of returns from validated orders at <i>θ</i> = 0.3. In the situation shown, where buyers are in the minority after validation of orders, all buyers find a trading partner (red). If all sellers could trade they would achieve the “desired” return distribution (light blue). But only a randomly selected fraction finds a trading partner, leading to the “realized” return distribution (dark blue); the other sellers receive a return of zero. The realized sellers’ return distribution has the same total area as the buyers’ return distribution as both represent the total number of trades.