A general volume-parameterized market making framework

We introduce a framework for automated market making for prediction markets, the volume parameterized market (VPM), in which securities are priced based on the market maker's current liabilities as well as the total volume of trade in the market. We provide a set of mathematical tools that can be used to analyze markets in this framework, and show that many existing market makers (including cost-function based markets [Chen and Pennock 2007; Abernethy et al. 2011, 2013], profit-charging markets [Othman and Sandholm 2012], and buy-only markets [Li and Vaughan 2013]) all fall into this framework as special cases. Using the framework, we design a new market maker, the perspective market, that satisfies four desirable properties (worst-case loss, no arbitrage, increasing liquidity, and shrinking spread) in the complex market setting, but fails to satisfy information incorporation. However, we show that the sacrifice of information incorporation is unavoidable: we prove an impossibility result showing that any market maker that prices securities based only on the trade history cannot satisfy all five properties simultaneously. Instead, we show that perspective markets may satisfy a weaker notion that we call center-price information incorporation.