Immigration activists hold signs outside the law firm Pillsbury Winthrop Shaw Pittman in Washington, D.C., where presumptive GOP presidential nominee Donald Trump was set to be deposed June 16 in his lawsuit against chef Geoffrey Zakarian for his pulling out from a restaurant at the Trump International Hotel in Washington. (Alex Wong/Getty Images)

Whether you like or hate Donald Trump, the presumptive Republican Party nominee for president, you can better understand his positions if you grasp two principles of game theory — that there are conditions when it is rational to be ambiguous, and conditions when it pays to be confrontational.

Much of what Donald Trump offers is ambiguity, which in part stems from his ignorance on policy issues. Game theory suggests that this is a useful stance when making deals. Trump combines ambiguity with confrontation, which works to draw out opponents on a battlefield on which Trump thinks he can win. The latter strategy is dangerous, however, if one is bluffing and the bluff is called. Let’s look at three elements of Trump’s game theory strategy (conscious or unconscious) in turn.

1. Unpredictability can be a rational strategy

Unpredictability is a rational strategy in games if you and your opponent have clashing interests, and your best choice and hers depends on what strategy each of you chooses. When choices are interdependent in this way, each side may intentionally be waiting to discern the other’s strategy to respond optimally. But if each side is determined to wait until the other side commits, game theory suggests that one should behave in a way that prevents an opponent from predicting exactly what you will do. That may include behaving randomly – because if your behavior is truly random, you will not be able to predict it yourself. And that makes it impossible for your opponent to outguess you.

Trump clearly grasps that unpredictability can leave an opponent guessing about what one might do. When questioned about whether he would shut down the government to pursue a cause, Trump declined to say, “because I want to show unpredictability.” He gave a similarly ambiguous response when asked whether he would use nuclear weapons to stop terrorists.

Leaving your choice to chance — in negotiations this may include walking away from the table, holding out longer, or offering a compromise settlement — can be both unnerving and effective. The uncertainty of your choice may force an impatient negotiator to move in your direction. However, it may also sabotage a deal. Appearing to be unpredictable is the essence of Trump’s approach to extracting the most from an opponent in difficult negotiations.

2. It may be rational to seem irrational

The second lesson from game theory is that it may sometimes be rational to be willing to do something outrageous and prepared to accept costs that objectively would seem to make no sense. Thus, Trump is known for being hard-nosed in almost all negotiations, making his toughness a predictable response to his opponents. Consider his willingness to declare bankruptcy in several business deals, which normally would sully a dealmaker’s reputation. And yet Trump has always managed to emerge from the ashes, as he announces in “Trump: The Art of the Comeback,” with a new face-saving deal.

This strategy is reminiscent of Richard Nixon’s “madman theory:” By credibly appearing to be mad, you strike fear in the heart of an opponent that you might do something dreadful, even at your own expense. True, bankruptcy hurts all parties, but they salvage something, which is better than losing everything by blindly forsaking this option.

3. Insisting on an extreme, even outrageous, position can force others to respond in ways that give you an advantage

This strategy reflects another principle of game theory. In some games, it’s best to be anything but ambiguous. Instead, one should take an unequivocal position and force an opponent to respond to it. Trump’s proposal to evict millions of Mexicans who are in the United States illegally, and force Mexico to pay for a wall that will keep them out in the future, is, as many have pointed out, completely impracticable. It will not happen, even if Trump is elected president.

Similarly, threatening to purge the judiciary of judges of Mexican or Muslim ancestry because they cannot be fair appears to many a reprehensible racist attack on our system of checks and balances. Trump says that his remarks on judges were “misconstrued,” but he has refused to apologize for this and many other intemperate remarks.

What purpose does his militancy serve? It forces people to respond, some with delight and some with outrage. To his supporters, it shows his strength and willingness to take a provocative position, even at the expense of alienating others. Trump’s demeaning comments on both his opponents and women convince many that he is a person to be reckoned with, as evidenced by his strong showings in the caucuses and primaries.

In effect, Trump is playing a game of chicken, daring those who oppose him to battle him on these issues. Sen. Marco Rubio (R-Fla.) was a candidate who stooped to Trump’s level in exchanging sexual taunts — and lost badly by undermining his image as an upright moderate.

These strategies don’t always work

This is not to say that a party that acts boldly, daring an opponent to respond, will always come out on top. In the 1962 Cuban missile crisis, the Soviet Union tried to counter the nuclear advantage of the United States by installing intermediate and medium-range nuclear missiles in Cuba.

The United States responded with a naval blockade of Cuba, euphemistically called a quarantine, forcing the Soviets to withdraw the missiles. But the “deal” also included a public pledge not to invade Cuba and a secret provision that the United States would remove its missiles from Turkey. Thereby a compromise may be achieved, even if it’s not the ideal one sought.

What do these strategies say about Trump?

Trump’s relish for provocative positions may continue through the campaign against Hilary Clinton. They may — emphasis on the conditional tense — subside if Trump wins the presidency. Then he could back off from his extreme stances by saying, in effect, that he was misconstrued or now has more important issues to attend to.

But Trump’s inability to apologize for anything, and his need to try to demolish opponents with invective and degrading labels, could backfire. It is not necessarily true, in Trump’s words, that what worked to win the pennant (primaries) will work to win the World Series (general election). Game theory says that reputation can be important in continuing battles. If he remains committed to the reputation he’s built so far, Trump may be too rigid to alter his strategy.

If he is too rigid, it may be useful to find that out now. Threatening to use nuclear weapons as president to induce your opponent to back off from a dire confrontation — and thereby risking a nuclear exchange — is gamesmanship on a different order of magnitude than threatening bankruptcy if your opponent doesn’t accept your terms.

A heady mix of ambiguity and provocation has worked brilliantly in helping Trump secure the Republican nomination. But this is only half the race. A good strategist must sometimes changes his tactics, and it’s not clear that Donald Trump will be able to do so.

Steven J. Brams is professor of politics at New York University and author of, among other books, “Game Theory and the Humanities: Bridging Two Worlds” (MIT Press, 2011). This is an updated and expanded version of an essay that appeared in Plus in May.