Coordination and conflict on self-resolving markets

1. The limits of externally resolved markets
In recent years, information markets (IMs)—markets for trading contracts regarding future or otherwise uncertain events—have proven highly reliable in making predictions in a wide variety of areas, ranging from politics and policy to sports, commerce, and medicine. Any explanation of why that is will have to appeal to the fact that such markets reward those who are right. So, for example, we might set up a market on the upcoming Presidential election in France. Bets on the candidate who wins will be rewarded; bets on the candidates who lose will not.

This is one way to settle trades on IMs: tie rewards on the market to the occurrence (or non-occurrence) of events external to the market. And having markets be externally resolved in this manner makes a lot of sense since it imposes a very straightforward form of discipline on the market, by creating clear incentives to those in the know to reveal their knowledge on the market.

But there’s also an obvious limitation to externally resolved IMs: they can only be used when waiting for some external event to resolve the market is an option. Sometimes it isn’t. Sometimes we want to predict events that are highly significant but far in the future—e.g., Will the UK leaving the EU turn out to have a big, negative net effect on the UK economy? Is this our last century?—or evaluate counterfactuals with clear implications for future policy—e.g., Would ISIS be around today, had Nouri al-Maliki’s government been more inclusive of Sunnis? Would the EU have been more successful in weathering the financial crisis, had it opted for a federal structure? and Would the current refugee crisis have been avoided, had western countries taken a different position on Bashar al-Assad early on during the civil war? Here, IMs will have to remain silent.

2. Self-resolving information markets
That is, unless there’s a way to set up self-resolving IMs, or SRIMs for short. SRIMs tie rewards, not to the occurrence of some event external to the market, but instead to events internal to the market. For example, a SRIM might settle bets with reference to the market value at some pre-specified time, unknown to the traders. Come that time, whatever the market value is, that's what determines who gets rewarded.

There's something slightly counter-intuitive about SRIMs. Traditional, externally resolved markets—let's call them TIMs—involve people betting on external events. On the face of it, however, SRIMs seem to involve people betting on what other people will be betting on, who in turn will be betting on what other people will be betting in... and so on. Why on earth should we expect such betting to tell us anything of predictive value?

The first thing to note is that such bets are, in a sense, extremely familiar. It's what we see on stock markets. Rewards and losses on a stock market are not determined through some great closing event, where the 'correct' value of each stock is revealed, and payments settled accordingly. No, rewards and losses are a function of continuous bets on what people will be prepared to pay for what in the future. So, when analysts speak of stocks being under- or overvalued, it's not that there's some underlying, 'correct' value offering a benchmark; they're simply expressing their expectations about who will want to pay what for what in the future.

Now, this is not to deny that trades on stock markets are, by convention, often grounded in considerations external to the markets, such as the fundamentals of the companies traded. If that were not so, it would be difficult to explain why things like large reported losses and corporate scandals should have such an impact on share prices. People treat such things as having a negative impact on share prices, and (rightly) expect that others will do the same—and what people are willing to pay for the relevant shares falls as a result. So, while stock markets are internally resolved, there's still a very real sense in which they're disciplined by external events in a way that creates incentives to those in the know to reveal their knowledge on the market.

3. Games of coordination and conflict
What about SRIMs, then? While there might not be any convention to trade with reference to fundamentals on SRIMs, there's reason to believe that such a convention will arise. To see why, notice that trading on SRIMs can be expected to take the form of a tacit coordination game (as Michael Abramovicz has suggested). For present purposes, a game is any interaction where your gain or loss is a function of the choices of others. Coordination games are games where gains or losses are determined specifically by your ability to coordinate your actions with others, and tacit coordination games ones where such coordination happens in the absence of agreements or explicit conventions. Take the following example from David Lewis's Convention (in turn borrowed from Thomas Schelling):

"Suppose you and I both want to meet each other. We will meet if and only if we go to the same place. It matters little to either of us where (within limits) he goes if he meets the other there. [...] The best place for me to go is the place where you will go, so I try to figure out where you will go and to go there myself. You do the same. Each chooses according to his expectations of the other's choice. If either succeeds, so does the other; the outcome is one we both desired" (Lewis 1969, p. 5).

Something similar holds for the type of game played by traders on a SRIM: since the final market value will be a function of the sum of individual trades, each person is going to want to place bets in accordance with how other people will be trading. Like the two of us when trying to meet, they're trying to figure out where people are heading, and to go there.

But note that SRIMs aren't pure coordination games; they're also games of conflict. Specifically, on the type of algorithm used on many IMs, high rewards are given to those who take high risks by moving the market a big distance towards the 'correct' value. In the case of SRIMs, that means being the first person to figure out what people will be coordinating on, and thereby getting a first mover advantage. So, on SRIMs, you don't simply want to be the one to show up where everyone else is bound (coordination); you want to get there first (conflict). And stock markets work the same way, of course: when buying stocks, it's not just that you want to buy what everyone else wants to buy; you want to buy it first.

4. The 'face value' hypothesis
By reflecting on this interplay between coordination and conflict we can now see why it's reasonable to expect that a convention will arise on SRIMs that mirrors the stock market convention of trading with reference to fundamentals. Because so long as you realize that your reward on a SRIM depends on your ability, not simply to predict any future coordination point, but also to be (among) the first one(s) to do so, you're going to want to move the market, if you're to trade at all. But move it with respect to what?

Well, strictly speaking: with respect to whatever you want. But remember what game you're playing here: you're trying to, in effect, figure out what other people will be doing on the market. So it will make little sense for you to pick a completely idiosyncratic consideration. To return to our analogy, when trying to coordinate a meeting place with you, were I to decide to go to some place that bears significance only to me, I'm likely to end up alone. To coordinate successfully, the place to which we should both be heading needs to somehow be salient to the both of us.

And here's a hypothesis: what's likely to be salient to all traders on a SRIM is the content of the question being bet on. Let's call this the 'face value' hypothesis. For example, is this our last century? Well, is it? If you think it is, then bet on that. If you don't think so, then that's your bet. If that's salient to you, most likely it will be salient to others as well—and, before you know it, you'll have coordinated your actions with others. And if so, you better get your bet in quickly, to ensure that you're the first one to go where others are bound. 

5. Self-resolving, but externally disciplined
So that's the convention that one can expect to develop on SRIMs: take the question at face value, and bet accordingly. Will it work? To answer that question, we would need to set up SRIMs and see how people actually respond to them. What's for sure is that, if the face value hypothesis is true—and that's a big if until we have some empirical data—then trading behaviour on SRIMs will be no different from than on TIMs, in which case we can bring the wealth of things we know about the latter to bear on the former.

For example, we know that TIMs tend to be driven by a minority of marginal traders. Such traders tend to trade higher‐than‐average sums, be active on the market on a higher‐than‐average number of days, show a lower‐than‐average degree of biases, and earn higher‐than‐average returns. Since they thereby have a disproportionally strong influence on the price signal, and the price signals of TIMs moreover tend to constitute accurate verdicts, we have reason to believe that the accuracy of TIMs are to a great extent due to the informed trades of marginal traders.

That's why, rather than saying that TIMs are successful on account of the wisdom of crowds, it seems more accurate to say that TIMs succeed by harnessing the wisdom in crowds, including in crowds where the majority is uninformed, and possibly systematically so. In fact, there is more direct evidence for this hypothesis. Oliven and Rietz found that, on the 1992 presidential vote share market on the Iowa Electronic Markets, the average error rate of market makers—the subset of marginal traders that are particularly active in setting bid and ask prices—was close to one‐sixth of that of the price takers—the traders who mostly accept others’ prices.

If the face value hypothesis is true, then we can expect similar trading behaviour on SRIMs, and specifically that the markets will be driven to a disproportionate extent by an informed minority of marginal traders. It's difficult to overstate how significant that would be. It would mean that SRIMs can be disciplined by external events without actually being resolved in terms of those events. We would, in short, have all the accuracy of TIMs, without their limitations—and the predictive power of markets could be extended to a whole host of significant issues on which TIMs have to remain silent, but SRIMs do not.

Kristoffer Ahlstrom-Vij