Republican presidential candidates Donald Trump, left, and Sen. Ted Cruz (R-Tex.) in the Fox Business Network Republican presidential debate. (Photo by Scott Olson/Getty Images)

As Jonathan Martin and Alexander Burns nicely detail in yesterday’s New York Times, the Republican “establishment” (alternatively referred to by Josh Voorhes in Slate as the “non-anti-establishment” vote) has a problem. Simply put, these folks would prefer anyone out of the Rubio/Christie/Kasich/Bush crowd to Trump or Cruz. But none of those four seems to be emerging as a clear favorite.

Even worse — but not surprising given the strategic imperative of needing to first win the “establishment primary” before going on to take on Trump or Cruz — these four seem to be spending most of their time attacking one another instead of Trump and Cruz. The fear, therefore, is that the window of opportunity for any of the four to emerge as a clear alternative to Trump or Cruz may be closing.

In the language of game theory, this is a focal point problem. If all the establishment voters/donors could agree on one of the “establishment four” candidates, that candidate could be a viable competitor to Trump and Cruz. But establishment voters/donors are uncertain about which one of the four that will be — and so votes and money get split.

The focal point was raised to prominence in game theory by Nobel laureate Thomas Schelling in his book “The Strategy of Conflict.” Schelling famously noted that if you ask someone where and when to meet someone else in New York City that — even without any other information — a non-trivial number of people would go to the information booth at Grand Central Station at noon. Simply because of its prominence in people’s minds, it emerges as a natural focal point, thus increasing the probability of coordination, which, crucially, is a net benefit to both of the people who are trying to find each other. In other words, this is not a “zero-sum” game, in which one person has to lose for another to gain.

The Republican establishment voters need a focal point.

The problem, of course, is that each of the “establishment four” thinks that he should be that focal point. Consequently, no focal point emerges. As Martin and Burns note, the great hope for the Republican establishment these days is that Iowa and New Hampshire will deliver that focal point. If one of the establishment four were to soundly beat the other three, then voters and donors would get their focal point and coordinate going forward. (Indeed, this is supposed to be one of the main reasons Iowa and New Hampshire get to vote before the other states.) In an ideal world for the Republican establishment, the other three would even drop out.

But what if no clear winner emerges? What if the question of which of the four should be the focal point is just as muddied after Iowa and New Hampshire as it was going in?

Here is a solution to this problem: The candidates themselves could agree to pick who drops out. We could imagine a number of mechanisms that could be used. The most obvious would be whoever “wins” New Hampshire and Iowa (e.g., whoever of the four gets the highest number of delegates from the two states combined) gets to stay in while the others drop out of the race. But anyone who thinks he is unlikely to win won’t agree to the deal. And there’s the question of whether New Hampshire and Iowa voters should have so much influence compared to those in the other 48 states (although — it should be noted — this is exactly what the establishment is hoping will happen).

An alternative — simply picking a name out of a hat — would likely not appeal to the presumptive front-runners.

A third option — a popularity weighted draw — might have just the right incentives to get all four on board. Imagine this: We have an urn with 100 ping-pong balls in it, each of which is labeled Bush, Rubio, Christie or Kasich. The number of balls that each candidate gets to put in the urn out of the 100 is based on three factors: (a) how well they do in Iowa, (b) how well they do in New Hampshire, and (c) how well they are doing in some set of national polls that are conducted over the seven days following the agreement. Before the drawing, the campaigns would agree on a formula to weight these three factors. Then after the Iowa, New Hampshire and poll results are known, a single winner is selected randomly from the urn, and the other three candidates drop out.

Why might the front-runners agree to such a deal? They would believe they would have the highest chance of winning the draw, and the prize of “winning” would suddenly be much more valuable: an automatic (and immediate) anointment as the establishment candidate, and therefore a much cleaner shot at beating Trump and Cruz.

Why might a candidate who (without publicly admitting it) thinks they are not going to do particularly well in the coming votes agree to this? They would believe that even if they have a low probability of winning the draw, it is probably a better shot at getting the nomination than they currently have.

Why might Republican establishment voters/donors agree to this deal? (Technically they wouldn’t have to agree to the deal for it to be made — only the candidates need to agree — but let’s just assume the candidates won’t make the deal if they believe voters and backers will punish them for making it.) As long as Republican establishment voters prefer one of the establishment four to Cruz or Trump significantly more than they care about which of the establishment four gets the nod, then this deal does exactly what they are hoping Iowa and New Hampshire will do: makes sure that Iowa and New Hampshire (plus the national polls) picks a focal point soon.

This arrangement also has the advantage of not needing the candidates themselves to have a realistic assessment of their likelihood of winning. It appeals to all the candidates, whether they think they are front-runners or laggards. So long as they are at least slightly risk averse — i.e., they don’t think they are 100 percent certain to come out of Iowa and New Hampshire as the undeniable focal point — it’s a good deal.

Game theory, however, presents one additional hurdle for the implementation of such an agreement, which is the credible commitment problem. More specifically, what’s to keep any of the candidates from reneging on the agreement to drop out if his name is not selected in the random draw? Fortunately, game theory also points to a solution here, which is to try to ex-ante raise the cost of reneging ex-post.

One way to increase the cost of ex-post reneging would be to focus on the political cost: the four candidates could have a very public press conference (in real life or online) in which they promise to “let the best person win,” explaining the deal and what they are planning to do and why. (As an aside, it would be fun to watch such a “unity rally” among candidates competing with each other). Following such an announcement, it might be politically impossible to go back on the deal.

But it would also be possible to impose a financial cost to the candidates. The candidates could all issue some form of very expensive bond or futures contract that they would be legally bound to pay off if they (a) lost the draw and (b) did not suspend their campaign immediately afterward. One could also imagine a similar arrangement involving a deposit of a substantial sum of money that would not be refunded if similar actions were not undertaken.

Of course, the big issue would be whether the advantage of guaranteeing a cleared field would be worth the cost of looking like this is yet another example of Washington politicians following their own interests at the expenses of the voters, particularly in a year where “anti-establishment” is already playing well. Would such an arrangement drive “establishment voters” into the anti-establishment camp? The question comes down to how certain the “establishment voters” are of their preference for one of the establishment four over Trump or Cruz. If those preferences are strong enough, then the risk might be worth taking. But if these voters could be pushed to Trump or Cruz (or someone else) if such a deal were made, then the deal would not make sense.

To be clear, I’m not arguing here that the candidates will agree to such a deal. I’m only illustrating how such a deal — guided by game theory —  among these candidates could solve some of the problems faced by their electorate.