Many people think that Donald Trump is crazy or irrational because he is apparently so impulsive. Social scientists might not be quite so quick to rush to judgment. One tool set we have for thinking about how rational actors behave in socially complex situations is game theory, mathematical theory of strategy.
So is Trump behaving in the ways that a game theorist would predict?
Answering that requires figuring out what his goals are, and whether he treats games as one-shot encounters, or as continuing interactions with one or more persons. (In this usage, a game is a situation in which the choices of all the participants, or players, determine the outcome.) Knowing Trump’s goals and time frame, we can assess whether his approach is rational in the game theoretic sense — that is, whether he chooses the best means to attain his goals.
Trump is an unusual politician
Trump’s goals differ radically from those of most politicians, who want to maximize their chances of reelection.
Even though the president has already launched his 2020 reelection campaign, he seems to dismiss his low approval ratings and is not attempting to attract support from beyond his existing base. If his low ratings — which he attributes to fake news and biased media — do not bother him, what are his actual goals?
Trump thinks he is playing a zero sum game all the time
The best way to think about his goals are to look at what he says. Trump’s self-stated goal is to win. He brooks no opposition, looking to beat those who challenge either his policies or his motives. He charges ahead and does not seem to worry much about the long-term consequences of his actions.
To a game theorist, this implies that he thinks he is playing a zero-sum game, in which completely crushing his opponents is everything. He leaves little if any room for compromise or negotiation, because in a Trumpian world, what he wins others must lose. “Zero sum game” is the theoretic term for a game in which the sum of the “payoffs” to the players is zero, so that every time one player gains it must correspond to someone else’s loss. Under this logic, every situation in which there is disagreement becomes a confrontation, from which there are only winners and losers.
However, he’s probably wrong
Other than sports competitions, most games in life are not zero sum. Of all the possible games with two players, each of whom can choose two strategies, 96 percent are not zero sum. There are four possible outcomes in these games, depending on the choices of each player, and in the vast majority the preferences of the players are not diametrically opposed.
In nearly all conceivable games, there is some room for compromise, allowing both players to benefit to some degree from a win-win outcome.
This is even true of notoriously antagonistic games as Prisoners’ Dilemma and Chicken. In Chicken, for example, two drivers speed toward each other on a narrow road. If neither swerves, they will collide and kill each other. If one swerves and the other doesn’t, both will live, which is better than dying — but the swerver will be disgraced.
The safer course in Chicken is for both players to swerve before the collision occurs. When John Kennedy and Nikita Khrushchev played nuclear chicken during the 1962 Cuban missile crisis, Kennedy made significant concessions in return for Khrushchev’s withdrawing Soviet missiles from Cuba. This was a win-win outcome, but one that came perilously close to a lose-lose nuclear disaster.
Backing off from a Chicken-type confrontation seems not to be in Trump’s DNA. He will always take the chance that he can force the other driver to swerve and thereby come out top dog — even if his opponent is a risk-taker and might also hang tough.
Trump relishes confrontation, as when he exchanged sexually suggestive taunts with Marco Rubio during the Republican primary debates. The aftermath of their exchange, however, was not a lose-lose outcome, as it would have been if they were playing Chicken. It was win-lose, because Rubio threw away his reputation as a morally upright moderate who would not stoop to Trump’s level, whereas Trump did not have that kind of reputation to lose. Appearing undaunted, he came out the winner.
His timeline is always short
Since ascending to the presidency, every encounter for Trump seems to be a one-shot battle. He doesn’t think much about the future or his reputation, except his reputation as a formidable player who will win every dispute.
Trump tries to burnish this self-perception as a winner through an unending stream of boasts (often false) about his greatness and the failures of all his previous and present antagonists, including Hillary Clinton and Republicans who question him, like Sen. John McCain. This may not result in long-term success, because outside the sports world, most win-lose outcomes are not stable. Even in zero sum games like sports, winning dynasties do not last forever, because winners become complacent, make mistakes, or miss innovations that their competitors find.
Other actors can start to push back
In politics, players in losing positions can often do better, even if only slightly, by changing their strategy. This is especially true when they are dealing with an inflexible opponent like Trump. Unlike Trump, most people don’t see the world as zero-sum. We see room for maneuver and compromise, even if this may be difficult to achieve in nonzero-sum games like Chicken.
How might opponents of Trump outmaneuver him in his self-constructed zero-sum world? The answer depends on whether Trump is right that a specific situation is indeed a zero sum game. When the game is zero sum, as with a congressional vote in which one side wins and the other loses, Trump’s opponents have limited options — although they could still look for a stable outcome (what game theorists call a “Nash equilibrium”), such as getting the vote delayed or postponed if they think they will lose.
If the conflict is not zero-sum, but Trump misreads his opponents’ goals and proceeds as if it were zero-sum, they should play the real game, but take into account that he views it as zero-sum. This would allow them to adopt realistic strategies while Trump’s misperceptions will get him into trouble.
For instance, more than once Trump has lambasted judges for ruling against him. Trump clearly thought of the interaction as a short-term zero sum encounter, in which either he or the judges lose.
In fact, this is a longer-term game. Attacks on judges may prove publicly unpopular and pave the way for long-term losses as courts dig in to oppose him. This would cause him difficulties, as he cannot easily ignore their rulings, given the checks and balances of our constitutional system. Richard Nixon, who was forced to resign the presidency in 1974, learned this to his chagrin.
Trump’s apparent need to win at all costs, and almost never by stealth, will surely lead to future grief for his presidency. But there is also the real danger that his blunt approach will have untoward consequences for the country and the world. His domestic opponents are not the only ones who can figure out ways to turn the tables on a strategically inflexible thinker.
Steven J. Brams is professor of politics at New York University and author of “Game Theory and the Humanities: Bridging Two Worlds” (MIT Press, 2011).