Regardless of the details, the quality of the deal depends on how much a Kasich exit matters to Mr. Rubio. The more crucial his exit, the stronger any promise is sure to be.

There is a third strategy available to Mr. Kasich, which takes the form of threats. Here, Mr. Kasich might insist on a promise or concession from Mr. Rubio; if he doesn’t get it, he could threaten to support a different candidate, like Mr. Trump or Mr. Cruz. That move wouldn’t serve shared establishment interests, but if the threat had the potential to damage Mr. Rubio enough, it could be a useful bargaining chip. “Being crazy is a strategy, but only if your opponent actually believes it,” Mr. Thaler said. Of the three strategies described here, this seems least likely.

Two external factors complicate this matter further.

Part of the reason this dilemma exists in the first place is that mainstream Republicans lack the unity or influence to compel any cooperation. After the New Hampshire primary, one Republican likened the battle among mainstream candidates to a hockey fight: “The gloves are off and the refs can’t get in the middle of it.” That’s exactly right.

If establishment Republicans had a clear, unimpeachable leader who was not a participant in the race, that person might be able to compel a candidate to drop out and support whomever the party determined to be strongest, allowing candidates who quit to save face by saying they did it for “the good of the party.” At the moment, no such leader exists for mainstream Republicans, resulting in a tragedy of the commons-like failure of collective action.

Second, this is a game that’s played just once. The chance to be your party’s nominee for president comes along only every four or eight years, even for the very luckiest candidates. If the candidates lived in a universe in which they could run for president hundreds of times, they might agree that, on average, their shared interests were better served by cooperating. Once in a while, Mr. Kasich might try to win the contest outright against long odds, but, on average, he would probably agree that cooperating, including alternating victories, was the best way to serve his and Mr. Rubio’s shared interests. Game theory shows that in iterated dilemmas, played many hundreds or thousands of times, cooperation is a very stable strategy — one reason it is so common in nature.

But this is not an iterated dilemma. It’s a one-time-only dilemma with a tremendous payoff for the winner. As much as Mr. Kasich might think about his legacy, the good of the party or even his own chances in 2020 or 2024, the future is very far away.

Ultimately, they risk an outcome neither he nor Mr. Rubio wants. As Daniel Diermeier, the dean of the public policy school at the University of Chicago, notes, “A very important lesson of game theory is that sometimes the world is a grim place.”