Better Pricing for Tournament Prediction Markets

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Last year while working out a few thoughts on arbitrage opportunities in basketball tournament prediction markets at Inkling, it occurred to me that the Inkling pricing mechanism was just a little bit off for such applications. The question is whether something better can be done. An answer comes from the folks at Yahoo Research: yes.

Inkling’s markets come in a couple of flavors, so far as I know all using an automated market maker based on a logarithmic market scoring rule (LMSR). In the multi-outcome case – for example, a market to pick the winner of a 65-team single elimination tournament – the market ensures that all prices sum to exactly 100. If a purchase of team A shares causes its share price to increase by 5, then the prices of all 64 other team shares will decrease by a total of 5.

The logic of the LMSR doesn’t tell you exactly how to redistribute the counter-balancing price decreases. In Inkling’s case they appear to redistribute the counter-balancing price movements in proportion to each team’s previous share price (so, for example, a team with an initial price of 10 would decrease twice as much as a team with a previous price of 5). While for generic multi-outcome prediction markets this approach seems reasonable, it doesn’t seem right for a tournament structure. (I raised this point in a comment posted here at Midas Oracle last September, and responses in that comment thread by David Pennock and Chris Hibbert were helpful.)

The problem arises for pricing tournament markets because the tournament structure imposes certain relationships between teams that the generic pricing rule ignores. Incorporating the structure into the price rule in principle seems like the way to go. Robin Hanson, in his original articles on the LMSR, suggests a Bayes net could be used in such cases. Now three scientists at Yahoo Research have shown this approach works.

In “Pricing Combinatorial Markets For Tournaments,” Yiling Chen, Sharad Goel and David Pennock demonstrate that the pricing problem involved in running a LMSR-based combinatorial market for tournaments is computationally tractable so long as the shares are defined in a particular manner. In the abstract the authors report, “This is the first example of a tractable market-maker driven combinatorial market.”

An introduction to the broader research effort at Yahoo describes the “Bracketology” project in a less technical manner:

Fantasy stock market games are all the rage with Internet users…. Though many types of exchanges abound, they all operate in a similar fashion.

For the most part, each bet is managed independently, even when the bets are logically related. For example, picking Duke to win the final game of the NCAA college basketball tournament in your online office pool will not change the odds of Duke winning any of its earlier round games, even though that pick implies that Duke will have had to win all of those games to get to the finals.

This approach struck the Yahoo! Research team of Yiling Chen, Sharad Goel, George Levchenko, David Pennock and Daniel Reeves as fundamentally flawed. In a research project called “Bracketology,” they set about to create a “combinatorial market” that spreads information appropriately across logically related bets.…

In a standard market design, there are only about 400 possible betting options for the 63-game [sic] NCAA basketball tournament. But in a combinatorial market, where many more combinations are possible, the number of potential combinations is billions of billions. “That’s why you’ll never see anyone get every game right,” says Goel.…

At its core, the Bracketology project is about using a combinatorial approach to aggregate opinions in a more efficient manner. “I view it as collaborative problem solving,” Goel explains. “This kind of market collects lots of opinions from lots of people who have lots of information sources, in order to accurately determine the perceived likelihood of an event.”

Now that they know they can manage a 65-team single elimination tournament, I wonder about more complicated tournament structures. For example, how about a prediction market asking which Major League Baseball teams will reach the playoffs? Eight teams total advance, three division leaders and a wild-card team from the National League and the same from the American League. The wild-card team is the team with the best overall record in the league excepting the three division winners.

In principle the MLB case seems doable, though it would be a lot more complicated that a mere 65-team tournament that has only billions of billions of possible outcomes.

[NOTE: A longer version of this post appeared at Knowledge Problem as “At the intersection of prediction markets and basketball tournaments.”]

CNN Political Market = soon, the Planet Earths most traded play-money prediction exchange -after HSX.

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CNN Political Market

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Introduction

The goal of CNN Political Market is to combine the opinions of a diverse group of people to try and predict the probability of an event occurring or the value of something. Why is this important? Because more often than not, a diverse group of people or &#8220-crowd&#8221- will generate a more accurate prediction than an individual or a small group of &#8220-like-minded&#8221- or &#8220-single-discipline&#8221- folks.

In business, politics, and culture, this can have big ramifications:
– Predictions often turn out to be more accurate than surveys and polls-
– More accurate forecasts affect how marketing dollars are spent, how many widgets should be built in the first run, etc.-
– Decision making is more democratized, giving everyone input where they may not have had it before-
– Markets can serve as on-going indicators for key performance metrics.

Frequently Asked Questions

These are answers to questions we receive on a regular basis.
Q: What if I forgot my username or password?
A: It&#8217-s easy, just click here and new information will be sent to the email address we have for you.

Markets and Trading
Q: How do the prices in a market change?
A: Markets are guided by the forces of supply and demand. Every time a user buys a share in a particular idea or outcome, that demand forces the price up a little. The more people buy, the higher the price becomes. If the price gets too high, people will do the natural, self-interested thing and sell their shares to get a profit (or sell shares that they don&#8217-t own on credit). Similarly, each time a user sells a share, the price goes back down some.

Q: My math says I can buy more shares than the system lets me. Why?
A: Remember that for each share you buy, the price goes up some. If you&#8217-re buying a lot of shares at once, the last share in your order might cost significantly more than the first.

Q: I sold a block of shares, but I got less money out of it than I thought I would.
A: Just like the market price increases you see when you purchase shares, each share you sell drives the market price for those shares down a little. If you&#8217-re selling a lot of shares, the last share you sell be worth much less than the first.

Q: I think the current price in a market is reflective of what the market is trying to predict. What do I do now?
A: The best thing to do is to hold onto your shares. If you try to sell them, the market price will start to go down and you won&#8217-t make as much profit as you could if you wait for the market to close.

Balances
Q: What is &#8220-on credit?&#8221-
A: When you sell shares on credit you are betting that the market price of a stock is going to go down instead of up. The idea is to sell shares you don&#8217-t have at a high price, and buy them back later once the market price has fallen. You get to keep the difference as profit.

Because you never know how high a price will go up, we&#8217-ve set up specific rules for selling shares on credit so you don&#8217-t get yourself in to trouble:
– You can buy back shares you bought on credit with the money in your bank.
There is a limit on how much stock you can sell on credit. You can figure out what that limit is by adding your available balance to the total value of shares you have bought. For example, if you have $10 available balance, and you also own $10 of stock, you can sell $20 of stock on credit. In other words, we try not to allow you to go in to debt by always protecting you against the worst possible scenario.

Q: How can I tell how much money I have?
A: Your balances are listed in the &#8220-total assets&#8221- box which you can find on your dashboard/portfolio. Your balance is also listed on each market trade page.

Q: How can I get more money?
A: You can earn money by trading wisely in markets. Look for good ideas that are undervalued, examine market descriptions for interesting things that others might not have noticed, or use your own unique, personal knowledge to make predictions that others can&#8217-t.

Q: What is the play money good for?
A: Status in the online trading community is based on how much money you have- just take a look at the &#8220-top traders.&#8221- The more money you have, the sooner everyone will begin to refer to you as &#8220-sage.&#8221-

Q: Can I give some of my money to another user?
A: Money is non-transferable – you must earn your own by trading.

Marketplace and Help
Q: The website looks a little funny. Is my computer supported?
A: We support the latest versions of Internet Explorer, Firefox, and Mozilla for Windows XP and 2000. For Mac OS X we support the latest versions of Safari, Firefox, and Mozilla. The application may work in alternate OSes and browsers, but we can&#8217-t make any promises.

CNN Political Market officially launches.

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As Chris alluded to a few days ago in a post, we&#8217-ve worked with CNN to launch a marketplace for this election season. A smattering of markets are available now with more to come, I&#8217-m told. So if you like trading in Inkling and want to participate in what I assume will quickly become our largest marketplace (it&#8217-s featured now on http://cnn.com and the inbound traffic is &#8220-remarkable&#8221- to say the least) you can go here: politicalmarket.cnn.com