In "How markets slowly digest changes in supply and demand" by JP Bouchaud, JD Farmer and F Lilo the authors asserts:
Noise trader models have been proposed to explain why market impact is a concave function of trading volume.
and then they provide some more details:
The standard explanation for this is that it is due to a mixture of informed and uninformed trading. If more informed traders use small trade sizes and less informed traders use large trade sizes, then small trades will cause larger price movement per share than large trades.
What "models" do they refer to?