The Dynamic Pari-Mutuel Market
Prediction markets for business also must overcome a much more practical problem: ensuring that markets have enough liquidity–that is, enough individuals who are willing to trade–to enable those who have or could develop information to trade on that information. It would be hazardous to extrapolate from the success, say, of TradeSports and infer that prediction markets will work well for business decision making. It is conceivable that virtually every business in the country might benefit from prediction markets targeted toward predictions that are of use to them, but few traders will be inherently interested in participating in these markets. As a result, these markets will require subsidies. In Chapter 2, I described one possible approach to subsidization, but that approach would generally still require a reasonable number of individuals who have enough information about a particular problem to trade with individuals with better information. Ideally, a market should produce predictions even when only a very small number of traders studies the relevant issues. David Pennock has offered a separate proposal for prediction market design that would solve the liquidity problem.19 (He also filed an application to patent his approach, so anyone wanting to use this approach might need to obtain a license.)20 A substantial challenge facing prediction markets is that transactions occur only when someone is willing to buy and someone else is willing to sell. In effect, the conflicting predictions of two different traders are required before a single data point can be added. Pennock imagines a system in which individuals could change the prediction market probabilities by making bets that are consistent with their own predictions, without needing to find someone to bet against them. He calls this system a dynamic pari-mutuel market. Pennock shows that a dynamic pari-mutuel market can be designed in such a way that from the perspective of a trader it appears to be the same as a continuous double auction, the traditional form of a prediction market. A trader can place an order to purchase or to sell shares, and in some cases transactions between traders will be completed, but in other cases a trader will be buying shares from the market sponsor, who in effect always acts as a market maker. Individuals who are familiar with traditionally structured prediction markets and securities trading mechanisms should thus be comfortable with the dynamic pari-mutuel market, although the internal workings are different. Pari-mutuel betting might seem to be an inappropriate choice for prediction markets that might involve only a small number of individuals, because racetrack betting generally involves very large numbers of individuals. Pari-mutuel betting, however, can work with one or more bettors, given the always lurking possibility that someone else will choose to bet, perhaps at the last possible instant. If I am the only bettor and pick a single outcome though that outcome is far from certain, then someone who restores the pari-mutuel predictions to their appropriate relative levels will generally make money from me. Thus, a pari-mutuel market itself might serve as a useful alternative to prediction markets in some situations. Should only one person participate, that person has an incentive to make an accurate probability estimate by distributing money among different possibilities. When a number of individuals are expected to participate, each bettor will have an incentive to place each dollar bet in a way that restores the market to the correct value. As we saw in Chapter 1, a problem with pari-mutuel betting markets is that individuals have no incentive to bet early. Pari-mutuel betting might produce accurate predictions eventually, but prediction markets are likely to produce more accurate forecasts over time. A corollary advantage is that someone who buys tradable contracts based on information not generally available can sell those tradable contracts once the market has absorbed and accepted the information, thus saving the trader from any risk associated with the actual probabilistic event being projected. The sequential nature of prediction markets conceivably also might improve final predictions. Especially in prediction markets with small numbers of participants, some individuals might gain reputations for accurate predictions, and thus traders can take reputation into account as another variable that will assist in making predictions. In a pari-mutuel market, anyone with a reputation for accuracy will have an incentive to bet anonymously or at the last minute, because each bettor benefits if the bets in the rest of the market are as far off from the best predictions as possible. Pennock’s paper suggests that with appropriate modifications, a pari-mutuel betting market can also provide accurate probability estimates over time and give incentives for individuals to trade on information as soon as they obtain it. In addition, such a market does not require that there be another trader with whom a particular trader’s request is matched, and it can thus overcome the problem of “thin markets” in which little trading takes place. In a standard pari-mutuel market, the cost of a bet on a particular outcome is fixed. In the dynamic pari-mutuel market, by contrast, the price of shares varies over time, with prices changing according to the current probability predictions of the market. Each share in a particular outcome, however, will receive an equal payout if the outcome occurs, regardless of the price at which shares are purchased. The changing prices allow for calculation of the market probability of an outcome at a particular time, using formulas that Pennock develops. There are a variety of possible approaches to designing a dynamic pari-mutuel market. Two design decisions are particularly critical. The first is whether the winning bets are refunded or simply added to the pool from which the winnings are eventually distributed. An advantage of refunding the winning bets is that it makes it impossible for anyone who has invested in the correct outcome to lose money. If the winning bet is not refunded, then it is possible (though unlikely as a practical matter) that someone who buys a share in the correct outcome at a high price will lose money if the share subsequently falls to a very low price before ultimately winning. There is no inherent reason, however, that this is essential to the market, and refunding bets complicates the mechanism somewhat. The second design decision is the way the price for a share should be determined at any given time. Assuming that there are two tradable contracts in the market, an attractive approach is for the system to adopt a price function that ensures that the ratio of the prices of the two tradable contracts will be equal to the ratio of the amounts wagered on them at any given time. With this or many other possible price functions, the greater the amount invested in an outcome, the cheaper will be the other outcomes in the market. Suppose, for example, that the dynamic pari-mutuel market is used to predict the outcome of a race between the turtle and the hare. Let us imagine that so far ten dollars has been invested on the turtle and five dollars has been invested on the hare. The imbalance in the betting indicates that the turtle is the favorite, and accordingly the cost of the turtle share will be twice the cost of the hare share. For various price functions, Pennock offers formulas for determining the price at any time for purchasing an infinitesimal fraction of a share, and he uses these formulas to derive other formulas for calculating the number of shares that can be purchased for a particular sum of money.21 Unfortunately, for the price function that equalizes price and investment ratios, Pennock was unable to derive an inverse function–that is, a formula for determining the amount of money that would be necessary for purchasing a particular number of shares. He notes, however, that it would be possible for a computer to calculate an approximation of this inverse function for any degree of precision. Finally, Pennock also offers simple formulas for calculating the market probability of any particular outcome. Of course, all of these numbers easily could be displayed on a computer screen without the user’s understanding the mechanics of the market. Some of Pennock’s formulas depend on a simple and probably defensible assumption, albeit one that Pennock concedes he was unable to prove. The assumption is that the expected value of the per share payout for an outcome at a particular time, if that outcome should occur, can be easily calculated as a ratio: the total amount invested in both outcomes divided by the number of shares in the particular outcome.22 For example, if the $10 invested in the turtle is split among 5 shares, the payout per share would be equal to $3 ($15/5), though the return might vary from share to share depending on initial purchase price. Pennock shows that this would certainly be true in the instant before the market closes, but the question is whether it is true more generally. In other words, would market prices follow a “random walk,” meaning that the current price provides the best prediction of the future price given available information? This is not true in the traditional pari-mutuel market because of the incentive to wait until the last moment to trade. Pennock surmises that this will be true in the dynamic market if traders are rational, though he does not prove it systematically. Empirical analysis of such markets might help determine whether this assumption is in fact true, though Pennock emphasizes that participants can play the game nonetheless,23 and it seems likely that the market probability estimates will represent true probabilities. At least one argument suggests that the dynamic market might not follow a random walk, however. In Pennock’s prediction market, the amount that is invested can only increase over time, just as in a traditional pari-mutuel betting market. An implication of this is that the market probability prediction will be less sensitive to an investment of a fixed amount of money later than it would have been earlier. The flip side of this is that when one believes that the market prediction diverges from the true value by a particular amount, when more money has been invested it will take a larger investment to correct the market price. One can therefore earn more profit on information that changes consensus predictions by a set amount later in the market. There might then be some incentive to wait to trade on information until later in the market. This incentive, however, is qualified, because if there is a danger that someone else might trade on the information in the interim, then the market will move closer to the trader’s expectation of the true value, and profit potential may be less. Moreover, it might sometimes be possible to move the market price more than once, if other traders do not recognize that the repeat player’s original trades are informed. In a traditional prediction market, by contrast, a trader ordinarily always has an incentive to trade on information immediately, unless for some reason the market is expected to provide substantially greater liquidity later on, for example, as traders mistakenly grow increasingly comfortable with a particular estimate. The subsidy method described in Chapter 2 tends to provide roughly equivalent liquidity at all times. Pennock’s prediction market has at least two technical complications. The first is how to deal with markets in which there are three or more outcomes, and the second is how to deal with markets that produce nonprobabilistic numeric estimates. In his patent application Pennock notes, “Some natural extensions . . . would handle more than two outcomes, or a continuous range of outcomes.”24 The key intuition is that purchasing a tradable contract corresponding to one of a number of outcomes amounts to betting against all of those outcomes. The calculations for market price and the market assessed probability therefore must take into account the total money invested and the number of shares in all of the other tradable contracts. Ideally, the market mechanism should allow someone to bet on two or more items simultaneously. A market with a continuous range of options could work simply by providing proportional payoffs to two tradable contracts. For example, if the number being predicted is between zero and one hundred and turns out to be sixty, then investors in one contract could receive 60 percent of the pool and investors in the other could receive 40 percent. An alternative approach would be to divide the relevant numeric range into a large number of subranges, perhaps one hundred, and allow betting on numerous subranges. This would allow traders to profit by improving the market estimate of the probability distribution.
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