Integrating Market Makers, Limit Orders, and Continuous Trade in Prediction Markets

We provide the first concrete algorithm for combining market makers and limit orders in a prediction market with continuous trade. Our mechanism is general enough to handle both bundle orders and arbitrary securities defined over combinatorial outcome spaces. We define the notion of an e-fair trading path, a path in security space along which no order executes at a price more than e above its limit, and every order executes when its market price falls more than e below its limit. We show that, under a certain supermodularity condition, a fair trading path exists for which the endpoint is efficient, but that under general conditions reaching an efficient endpoint via an e-fair trading path is not possible. We develop an algorithm for operating a continuous market maker with limit orders that respects the e-fairness conditions in the general case. We conduct simulations of our algorithm using real combinatorial predictions made during the 2008 US presidential election and evaluate it against a natural baseline according to trading volume, social welfare, and violations of the two fairness conditions.