Smarket is an interesting new market that lets you bet on whether the rank of books and other products on Amazon will go up or down. This is another addition to a type of market I don’t think there’s a good theory for yet; markets with open-ended pricing. There are several other examples including the Hollywood Stock Exchange (HSX), ProTrade, and Yahoo!’s Tech Buzz Game. These markets all try to follow the real-world rise and fall of some abstract value (box office returns, on-field athletic performance, and search rank, respectively), and allow traders to bet on them.

So far, all the markets of this type use only play money, and that’s part of what I’m talking about when I say there’s no theory. One of the innovations that makes standard Prediction Markets (of the kind I described last week) workable is that a risk-neutral market operator can sponsor a market without taking a position in the trading; that is, without taking on risk. The traders buy and sell from one another, and the operator merely facilitates the trades. Even if you add an automated market maker, you can constrain the potential costs, while still facilitating unlimited trading.

Traditional bookies learned to handicap the events they were selling bets on or they went out of business quickly. Part of the development of insurance was inventing the actuarial techniques that allowed insurers to reliably estimate how their exposure would change as they sold various policies. Modern stock markets only allow short selling when the investors back their trading with assets that the broker can rely on if prices go the wrong way. Real money prediction market operators will need the same ability to constrain losses.

With the open-ended markets, the value to be paid out to stocks that gained isn’t limited, and isn’t related in a simple way to the price paid by the purchasers. I would expect a theory that showed how the market’s exposure is limited to start from the observation that one asset can only rise in value when another falls. This is true of Smarkets and TechBuzz because they’re based on relative rankings. It’s not obvious whether it’s true of HSX (Box Offices returns are only weakly limited) or ProTrade (the formulas for ranking athletes haven’t been published.)

It’s also not clear how to read the market results as predictions. In a standard Prediction Market, the traders’ incentive is to bid the price up or down until it matches the subjective probability, so prices should equal probabilities. David Pennock says the optimum target on TechBuzz is the square root of the search share. I think a separate analysis will have to be done of each institution, and if the rule isn’t easy to understand, it will be hard to claim that traders are producing prices that follow an optimum rule.

There also isn’t yet any theory regarding the feedback from underlying value to market value. Most of these markets seem to reflect changes in the underlying value by paying dividends to holders of the assets. Sometimes they (also? instead?) change the market maker’s current price for the asset. I expect this to make it difficult to come up with closed-form expressions of how the market operator’s exposure changes when assets are revalued. Remember that there’s no guarantee that similar amounts of money are invested in each market, or each side of any particular issue. And this kind of distinction is where the money pump was discovered in the TechBuzz Dynamic Parimutuel Mechanism. You can’t do this with real money if you don’t know what your exposure is.

These markets are definitely interesting. They allow Surowiecki’s Wisdom of Crowds to give us a hint about the rising and falling fortunes of things we care about. I welcome efforts to turn them into markets that can make predictions, or allow insurance, hedging, and the other side effects we expect from standard Prediction Markets.

Hat tip to Dave Pennock.