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.)