The most famous game-theory formula was developed in 1950, by two mathematicians, Melvin Dresher and Merrill Flood. But it was only later that another mathematician gave it the catchy name that made it famous: the Prisoner’s Dilemma. The idea is simple: two accused criminals have been arrested and are being interrogated separately. If they both stay silent, they’ll both get a year in jail. But, if one rats out the other, he could get away scot-free while his accomplice would spend three years in jail. The optimal outcome, in terms of total time served, is for both to remain silent. But, as Drescher and Flood posited, there is enormous likelihood that each will rat out the other. There are endless variations of the formula, tweaking the costs and benefits of silence and confession, but the core insight remains: if two people whose interests are mutually dependent on the actions of the other don’t fully trust each other, and don’t have the opportunity to secretly coördinate, they will end up behaving in ways that hurt both of them.

President Donald Trump and his former attorney Michael Cohen are currently playing out the Prisoner’s Dilemma in the most public and consequential way possible. (My colleague John Cassidy used game theory to explain the many leaks coming from the Trump White House this spring.) Cohen was, of course, Trump’s fixer, who handled hush payments to the porn star Stormy Daniels, and who likely knows of other secret activities carried out by Trump. Cohen was also an important intermediary between Trump and several of the oligarchs Trump dealt with in Russia and other former Soviet countries, and would know of any deals he made in the region in the decade before he became President. Many people assume that Cohen has an enormous amount of information that could shed light on Trump’s relationship with Russia, suspicious business activity, and, possibly, corruption in office. Cohen, after all, received millions of dollars from companies seeking his help in influencing Trump’s Administration. Cohen also held meetings with some of these new clients in Trump Tower. It would be a dramatic shift in Trump’s approach to business to allow his subordinate to profit from his name without some benefit to himself. It seems reasonable to imagine that Cohen may well have information that could damage, or even destroy, Trump’s Presidency. Yet what Cohen, in fact, knows remains a mystery.

Trump, for his part, has enormous power to punish or reward Cohen. As President, Trump can pardon him or use the full law-enforcement power of the federal government to punish him.

We are witnessing a grand, public Prisoner’s Dilemma, in which each man could, theoretically, destroy the other. Or, perhaps, they could work together to explain away any troubling information that comes out of the investigation of Cohen’s files. They can’t talk privately, because every interaction is likely to be scrutinized. Instead, they speak to each other through the media.

On Sunday morning, George Stephanopoulos reported on a lengthy conversation he held with Cohen, the first such interview Cohen has given since his office, home, and hotel room were searched by F.B.I. agents, in April. The interview appeared to dramatically shift the playing field against the President. When asked if he was still loyal to the President, Cohen replied, “To be crystal clear, my wife, my daughter and my son, and this country have my first loyalty.” He also gave other signs that he was no longer interested in publicly proclaiming his loyalty to the President, saying that Trump was wrong to call the ongoing Mueller investigation a “witch hunt” and to disparage the F.B.I. for investigating Cohen.

Emily Jane Fox, of Vanity Fair, reported last week that Cohen has begun to wonder if his fate is not as grim as so many imagine. If he turns on the President, he could become a hero, a man like the former Nixon aide John Dean, who admitted to wrongdoing and helped stop a corrupt President.

The Prisoner’s Dilemma shows that minor shifts in incentives can have an outsized impact on the choices people make. It also shows that, when two players cannot openly communicate, even the slightest hint of information from one player can have an enormous effect on the other’s choices. In this, Cohen seems to have made what game theorists call a “binding commitment,” a sign that he will pursue the benefits of coöperating against Trump. He has removed options from himself and from the President. It will now be harder for Cohen to revert to his previous state of complete fealty to his former boss. And he has made it more difficult for Trump to pardon him without appearing to mount a cover-up. It seems fairly clear: Cohen is willing to turn against the President. The key question now is what does Cohen know and what can he prove?

Trump’s path is clear now, too. If coöperation is no longer an option, he must destroy Cohen. He must crush this man’s credibility and find some way to so raise the cost of Cohen’s coöperation with Mueller that Cohen will remain silent. What will Trump do if he is convinced that Cohen does have information that could end his Presidency and destroy his family? Trump’s actions against Cohen and Mueller in the weeks ahead will give us clues regarding the President’s guilt.