Another play money arbitrage explanation, much easier than the last one.

I sat down to the computer this morning at exactly the time emails were arriving from Media Predict announcing the opening of five new markets for the &#8220-Project Publish&#8221- finalists. One of the five finalists will receive a book deal.

In the prediction markets, five new shares were launched at $50 ($ = Media Predict play money). Shares held in the winning book will be paid $100, the others will expire at $0. So, at market launch, selling one each of the five shares would gain $250, and guarantee a payoff of $-100. Result: riskless profit of $150. The market should have launched at $20 each (or, at least, that is one set of prices that would have eliminated the riskless arbitrage opportunity).

First to the new markets, I sold short what I could afford across the board, bringing all the prices down to $35. An hour or two later prices had drifted up on several shares, no doubt due to the enthusiasm some trader had developed for the books, but in their enthusiasm they didn’t realize that they should complement a purchase of one share with sales of other shares – otherwise they leave free arbitrage opportunities in the market. A bit later someone came along and sold all of the share prices down to $20 each.

Now, several hours later, prices have moved much higher on three of the books, while two seem to be drifting lower. I’ve sold some other Media Predict holdings so I could arbitrage some more, but I’m credit constrained in the Media Predict economy so I can’t grab all of the riskless profit. As I write, the current gain from selling a one-of-each suite of shares is $156, so the present riskless profit available is $56.

While the book shares are presented as five parallel markets, actually we have a single multi-outcome market. There are five books, and only one of the five will be selected. Since the sum of the probabilities across the five books is constant, if you think option A is more likely to win then it must be the case that the joint probability of B, C, D, and E is less likely. The market can take advantage of that relationship to improve market performance, for reasons that Chris Hibbert explains in “Increasing Liquidity in Multi-Outcome Claims.” If the market won’t do it, arbitrageurs can.

Note: Chris Masse was puzzled about bigger picture issues in his earlier post on Media Predict, and I comment on some of those issues in response. For the purposes of the post above I’m ignoring the big picture and just wondering about the market mechanism and implementation.

Dave Pennock and Rahul Sami have written a book chapter on Computational Aspects of Prediction Markets. It focuses on computability and complexity issues in markets that handle combination, conditional and compound orders. The article talks about the costs for the auctioneer, and presents the Logarithmic Market Scoring Rule and the Dynamic Parimutuel Auction as two feasible approaches to offering combination or compound markets.

The article is written for (and probably only accessible to) people who understand the language of computability and complexity theory. It does review the economic principles underlying prediction market mechanisms beyond call auctions and the double auction, but only sufficiently to introduce them to Computer Science people who are new to this application area.

The chapter closes with a list of open questions, and I&#8217-d like to highlight a couple of them:

1. &#8220-Are there less expressive bidding languages that admit polynomial matching algorithms yet are still practically useful and interesting?&#8221- If someone can find a feasible mechanism that supports an interesting subset of a complete combinatorial or conditional claims, we could run markets that provide answers to much more interesting questions.
2. The idea of betting on outcome permutations is intriguing. (Apparently I missed this paper at the recent conference in San Diego.)
3. &#8220-What is the complexity of finding a match between a single new order and a set of old orders known to have no matches among them?&#8221- I&#8217-m more interested in finding cheap solutions or new ways to pose the problem that are more tractable, but determining the complexity is the first step in the crowd Sami and Pennock are talking to.
4. &#8220-The model in Section 1.5 directly assumes that agents bid truthfully. Is there a tractable model that assumes only rationality and solves for the resulting game-theoretic solution strategy?&#8221- Wouldn&#8217-t proving incentive compatibility be sufficient to establish that rational agents would bid truthfully? I expect LMSR to be incentive compatible, though I don&#8217-t know how hard the proof is. I have a vaguer feeling that the Dynamic Parimutuel might also be incentive compatible, though I think the fact that the price isn&#8217-t directly a probability makes the link more tenuous.

I hope the inclusion of this chapter in what appears to be a broad work on computability, efficiency, and algorithm design in games, negotiations, markets, and networks will lead to new ideas that will expand the set of alternative market designs we can make use of. (I have linked to the chapter above- if you want to download the whole book, Pennock&#8217-s blog contains the password that you&#8217-ll need.)

Koleman Strumpf&#8217-s conference webpage:

Prediction markets are a tool for harnessing the wisdom of crowds. Recently, firms have begun to use these markets to leverage the information dispersed among their employees and customers. The markets have been used to improve forecasts of uncertain events, to generate new ideas, and to improve resource allocation within the firm. Prediction markets have great promise for helping firms manage risk, because they can provide more precise estimates of events which are both internal and external to the firm.

Bet2Give&#8217-s user guide:

What is a prediction market?

In a prediction market, traders buy and sell shares of a stock whose closing price is determined by a real-world event in the future. For example, each share of the Clinton Stock will be worth $1 if Hillary Clinton is the Democratic nominee for president in 2008, otherwise, it will be worthless. If you buy the stock at, say, $0.60, and Clinton goes on to win the nomination, then the stock will be worth $1 and you&#8217-ll have made a profit of $0.40 on each share that you bought. Well done!

However, you don&#8217-t have to wait for the stock to expire before making a profit. You can resell your shares at any time, hopefully for a higher price than what you paid for them. Buy low, sell high, it&#8217-s the secret of success.

Prediction markets offer a most entertaining form of betting directly against other people, with no &#8220-middle man&#8221-. They also allow exciting real-time betting during live events such as sports games. Finally, because, you can &#8220-resell&#8221- your bets at any time, the market allows you to control your risk precisely or to cut your losses. This may not be your usual way of placing bets, but it&#8217-s easy to learn and it&#8217-s well worth it for all the reasons above.

How to trade

bet2give()bet2give is a so-called &#8220-double auction&#8221- market, where each participant makes offers to buy and sell the stock at his or her chosen price. When a buyer&#8217-s price matches a seller&#8217-s, a trade happens.

To make a &#8220-buy&#8221- offer, you specify the price you&#8217-re willing to pay for the stock and the number of shares you want to acquire. To make a &#8220-sell&#8221- offer, you specify the price you want to sell your shares at, and a number of shares.

When you send your order to the market, it is entered into the &#8220-order book&#8221- where it joins the pool of other participants&#8217- offers. The offers are sorted by price, so that the best-priced offers to buy or sell are always given trading priority: When the highest-priced &#8220-buy&#8221- offer matches the lowest-priced &#8220-sell&#8221- offer, a trade happens whereby the buyer and seller exchange shares for cash.

Buyers and sellers must agree on price, but they don&#8217-t have to agree on the number of shares being traded. For instance, if the buyer wants 10 shares and the seller is only offering 6, then only those 6 shares are traded and the rest of the buyer&#8217-s offer, for another 4 shares, stays in the order book.

If your offer is priced too high or too low to find a counterpart immediately, it stays visible to all in the order book. It may find a counterpart later if the market moves your way, or you may also cancel it whenever you want.

Trading Strategies

While the outcome is undecided, the market stays open and the trading price moves up and down following supply and demand from the participants. Then, when the market closes, the shares you own are redeemed at the appropriate payoff value.

Strategy 1: Buy low, sell high: The usual way to make money in the market is to &#8220-buy low, sell high.&#8221- This means either buying shares at a lower price than their final payoff value, or buying shares only to sell them back later at a higher price to other participants.

Obviously, the &#8220-buy low, sell high&#8221- strategy only works if the trading price eventually goes up after you buy. If that&#8217-s not the case, you will lose money, but you can still try to cut your losses by selling your shares sooner than later:

Strategy 2: Pre-sell high, buy low: You&#8217-ll want to apply this reverse strategy if you think that the trading price will go down or that the payoff value will be lower than the current trading price. In essence, the market lets you sell shares that you do not yet own, under the strict condition that you must buy them back later. You are hoping, of course, that the price will fall in the meantime so that you can buy the shares back for less money than what you sold them for and pocket the difference.

You are free to choose when to do the buy-back, but if you haven&#8217-t done so by the time the market closes, you will have to buy the shares at the closing price.

How does it work? Technically, pre-selling shares you don&#8217-t own is called &#8220-shorting&#8221- or &#8220-going short,&#8221- and buying them back later is called &#8220-covering your shorts.&#8221- When you go short, you immediately pocket the amount of the sale, but the market also preemptively withholds from your account the maximum potential amount that may be required for the buy-back . Then, when you decide to cover your shorts, the cash that was withheld earlier is automatically used towards that purchase, and you get a refund for the money that wasn&#8217-t used.

In the end, your profit or loss is exactly the difference between the proceeds of the initial sale and the cost of the later buy-back. If the trading price has fallen in the meantime, you make a profit, otherwise, you take a loss.

Strategy 3: Buy a basket: In some cases, like elections, several stocks may be competing against each other so that only one of them will expire at $1 while the others will all expire at $0. In such cases, we give you the possibility to buy baskets of shares containing exactly one share of each stock, for $1. You can then dump the shares you presume will be losers onto unsuspecting buyers, and keep those that you think have a good chance of expiring at $1.

Experienced traders also view this as a cheap way to &#8220-short&#8221- several stocks at once.

The value of your holdings

Your holdings are the shares that you own in each stock, or the shares that you have pre-sold (your shorts). For each stock, the value of your holdings is estimated from the last trading price like this:

• A share&#8217-s current worth is estimated to be exactly the price at which the last trade occured.
• A short&#8217-s worth is estimated to be the difference between the maximum potential value of a share and the last trading price.

Of course, this is only an estimation. The actual liquidation value of your holdings will be determined by the price at which you are effectively able to sell your shares or cover your shorts when you decide to do so.

Liquidifying share/short pairs

If you do many trades, you may encounter a situation in which your portfolio contains both shares owned and shares pre-sold of the same stock. In this case, rather than having to buy-back the shares you pre-sold with cash, you can just use the shares you already own. Each pair of shares owned and pre-sold can be exchanged for exactly the maximum potential value of a share in cash.

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tion markets by foundations and think tanks.