Two things worth noting:
- The contract on each contender pays $1 whether the candidate gets a sole or a joint prize
- The set of contracts obviously does not span the space: it's entirely possible that none of the listed contenders wins the prize and it's instead awarded to something like Kitoyaki & Moore or three random econometricians not including Deaton.
So the sum of prices ought be around $0.9. Except that we can have multiple winners. If Thaler wins with Shiller, then the sum of payouts is $2. A Thaler/Shiller/Fehr prize would have it at $3. A Hart & Moore prize would have it at $1 as Moore isn't listed, but a Hart & Tirole prize would have it at $2.
How can we think about rational prices in this world, in terms of looking for arbitrage opportunities if the sum of prices is out of whack?
The sum of prices ought to be equal to:
- The sum of the probability of each as a single winner times $1, plus
- The sum of the probability of each as a joint winner with someone else on the list times another dollar for each in such a set.
The sum of current market prices is $1.92. Is that too high or too low if you think the probability of "none of the above" is 10%? I think it's rather too high: it's basically priced in that there is very likely to be a joint prize to two of the people on the list.
Now, I don't know the probabilities of joint versus single prizes. But here's another way of looking at it. Suppose you think that Shiller might get the prize, but that he's really unlikely to get it without Thaler. There's a decent chance of a Thaler prize without Shiller, but it's hard to imagine a Shiller prize without Thaler. We can then figure that the probability of Shiller winning is some fraction of the probability of Thaler winning. Drop Shiller out of the set of prices entirely and think only about a Thaler-only prize. Same for Nordhaus: we can imagine a Weitzman prize without Nordhaus, but not Nordhaus without Weitzman, though a joint prize is there most likely. The Nordhaus price ought then be lower than Weitzman and ought be ignored.
Get the set of all "most likely" guys for single prizes, or the part of pairs that is most likely. The prices of those singles ought to sum to one, or one minus "something else".
The sum of Thaler (drop Shiller and Fehr), Weitzman (drop Nordhaus), Hart (drop Tirole), Deaton, Posner (drop Peltzman, Tullock), Grossman, Dixit, Barro and Fama should then not be greater than one unless you can imagine a joint Thaler/Weitzman prize, or a Hart/Deaton prize, or a Thaler/Dixit prize. The odds of those odd combos is sufficiently low to be ignored.
If we take the sum above, we get $1.16 where it ought to be around $0.9 if we think that none of the guys whose prices we've kept are going to win in combination with other guys whose names we've kept. Of course, this biases things in favour of the sum of prices being low - Peltzman and Tullock are low probability chances, but I'm certainly not convinced that they couldn't get it without Posner. And there's a really good shot of Tirole getting a solo prize rather than joint with Hart. But I want to make it hard to show that the sum of prices is too high because I don't want to make a mistake in shorting a set of contracts that seems overpriced.
The best shot at an oddball combo? Fama/Shiller for finance. It would give Fama his due but take the sting off of "efficient markets" stuff by throwing Shiller in. Like the Hayek prize that was joint with Myrdal, except that Shiller is more deserving than Myrdal was. If that's a serious risk, then the sum of prices on the contracts still oughtn't be much affected as Fama is in there and Shiller's already dropped; I'd just previously been wrong in thinking Fama had zero chance. He has a chance, with Shiller.
If the sum of prices is $1.16 and ought to be around 0.9, then I ought to short the set of (Thaler, Weitzman, hart, Deaton, Posner, Grossman, Dixit, Barro, Fama) considerably, then short Shiller to keep his price relative to Thaler in line with the prices ex ante, Tirole relative to Hart, Nordhaus relative to Weitzman, and so on. The whole thing resolves Monday night, so capital isn't tied up all that long. Hmm.