John Salvatier has drawn my attention to a paper describing A Practical Liquidity-Sensitive Automated Market Maker [pdf] which fixes some of the drawbacks of the Automated Market Maker that Robin Hanson proposed.
Most importantly, it provides a good chance that the market maker makes money in roughly the manner that a profit-oriented human market maker would.
It starts out by providing a small amount of liquidity, and increases the amount of liquidity it provides as it profits from providing liquidity. This allows markets to initially make large moves in response to a small amount of trading volume, and then as a trading range develops that reflects agreement among traders, it takes increasingly large amounts of money to move the price.
A disadvantage of following this approach is that it provides little reward to being one of the first traders. If traders need to do a fair amount of research to evaluate the contract being traded, it may be that nobody is willing to inform himself without an expectation that trading volume will become significant. Robin Hanson’s version of the market maker is designed to subsidize this research. If we can predict that several traders will actively trade the contract without a clear-cut subsidy, then the liquidity-sensitive version of the market maker is likely to be appropriate. If we can predict that a subsidy is needed to generate trading activity, then the best approach is likely to be some combination of the two versions. The difficulty of predicting how much subsidy is needed to generate trading volume leaves much uncertainty.
I've reread the paper more carefully in response to John's question, and I see I was confused by the reference to "a variable b(q) that increases with market volume". It seems that it is almost unrelated to what I think of as market volume, and is probably better described as related to the market maker's holdings.
That means that the subsidy is less concentrated on later trading than I originally thought. If the first trader moves the price most of the way to the final price, he gets most of the subsidy. If the first trader is hesitant and wants to see that other traders don't quickly find information that causes them to bet much against the first trader, then the first trader probably gets a good deal less subsidy under the new algorithm. The latter comes closer to describing how I approach trading on an Intrade contract where I'm the first to place orders.
I also wonder about the paper's goal of preserving path independence. It seems to provide some mathematical elegance, but I suspect the market maker can do better if it is allowed to make a profit if the market cycles back to a prior state.