Making profit in a prediction market

Suppose one would like to estimate the outcome distribution of an uncertain event in the future. One way to do this is to ask for a collective estimate from many people, and prediction markets can be used to achieve such a task. By selling securities corresponding to the possible outcomes, one can infer traders' collective estimate from the market price if it is updated properly. In this paper, we study prediction markets from the perspectives of both traders and market makers. First, we show that in any prediction market, a trader has a betting strategy which can guarantee a positive expected profit for him when his estimate about the outcome distribution is more accurate than that from the market price. Next, assuming traders playing such a strategy, we propose a market which can update its price to converge quickly to the average estimate of all traders if the average estimate evolves smoothly. Finally, we show that a trader in our market can guarantee a positive expected profit when his estimate is more accurate than the average estimate of all traders if the average estimate again evolves in a smooth way.