But what if a scenario arose in which those assumptions failed? Here’s where elephants come into play. To achieve their mating goals, male elephants will sometimes play games of chicken, with one individual essentially giving the impression that he is crazy and has become an irrational player in a game premised on shared rationality and predictability.

It’s a tactic that works surprisingly well, because male elephants can in fact become temporarily “crazy.” One of the most terrifying sights in the animal world is an elephant in a state of must: Huge bulls, oozing a weird, foul-smelling, greenish glop from glands near their eyes, behave with violent abandon, taking risks and defying the basic rules of pachyderm propriety (and also giving rise to the term “rogue elephant”). Facing an elephant in must, other elephants — not to mention people — are well advised to get out of the way.

A similar problem arose in nuclear strategy in the 1990s. For all the comparable craziness of mutually assured destruction during the cold war, planners could safely assume that American and Soviet leaders would act more or less rationally. But what if a rogue state or a terrorist cell got its hands on a nuclear weapon? The rules of classic game theory would no longer apply.

In either case, whether you’re confronting a rogue elephant or a rogue nuclear state, the advice is the same: stop playing the game. Avoid the elephant or shoot it; politically isolate the rogue state or use military force to disarm it.

What does all this mean for the debt-ceiling debate? So far, President Obama and the Democrats have insisted on negotiations, assuming that the looming threat of debt default would force the Republicans to cave in on their strident demands and accept a compromise.

Instead, given the Republicans’ continued insistence on an unobtainable wish list of spending cuts and constitutional amendments, it’s fair to conclude that Mr. Obama is facing the political equivalent of an elephant in must — a player who simply won’t play the game.

In the 1983 movie “WarGames,” an errant military supercomputer has a final moment of lucidity in which it notes, “The only winning move is not to play.” The president is best advised to do the same: declare that the other side has foregone all pretense at rational legitimacy, and simply proceed to govern as best he can for the good of the country.