Donald Trump and game theory: Expert says no brilliant 3-D chess is involved

NYU game-theory scholar Steven Brams says Trump's unpredictability would work better in poker than in politics

By Chauncey DeVega

Senior Writer

Published September 20, 2019 7:00AM (EDT)

Donald Trump (Getty Images/Salon)
Donald Trump (Getty Images/Salon)

Politics is often conceived as a type of game. To win, a person or group must amass more power than the other players in order to advance their own goals. Victory can be achieved through cooperation with the other players, domination over them or some combination of the two.

Alternatively, a person or group can decide not to participate in this current version of politics, while they seek to invent their own game with different rules.

The rules of the game are determined by the structure of the political system. The players in the game send signals to one another as a means of determining whether they will cooperate or compete. The players must also decide how (or if) they will follow the rules of the game.

The game of politics is played both domestically and internationally. The latter takes the form of treaties, alliances, transnational movements, and other ways of coordinating and structuring a relationship.

Both elites and average people participate in the game of politics. However, the ability to influence the outcome of the game is not shared equally. Elites can rig the rules of the game to their own benefit — while still announcing that the game is fair and their victory was justified. Average people must find ways to negotiate and triumph in a game where the odds, more often than not, are skewed against them.

In the current game of American politics, is President Trump — as some observers have suggested — playing an elaborate game (often analogized as "three-dimensional chess") that the Democrats and his other rivals are unable to comprehend? Or is Trump just muddling through on instinct and force of will as he smashes the game of American politics in an effort to remold it to his desires and dreams?

In an effort to answer these questions I recently spoke with Steven Brams. He is a professor of politics at New York University and the author of numerous articles and books including “Theory of Moves,” “Game Theory and the Humanities,” “Game Theory and Politics” and “Mathematics and Democracy.”

In our conversation, Brams explains how game theory — a conceptual framework for studying the rational and strategic decision-making behavior of individuals and groups — can help the public understand the apparent contradictions of Donald Trump's presidency. He also explores what insights game theory can offer into Trump’s approach to Iran and North Korea. Brams also discusses how game theory can inform the public’s understanding of Nancy Pelosi and the Democratic Party’s cautious approach to the question of impeachingTrump, as well as Trump's efforts to defy them.

What is game theory? And how does it apply to politics?

Game theory can be defined simply as the analysis of interdependent decisions, which means that your best choice does not depend on what you unilaterally choose. It also depends on one or more other players. So there's this interdependence among choices, and the theory really is about trying to sort these out to determine better and worse strategies for players.

How do you model the behavior of someone who appears to be as unpredictable as Donald Trump? Is Trump playing some type of deep game of "3-D chess," as some observers have claimed?

Game theory has this notion of mixed strategies, which means you randomize. Sometimes you choose one strategy, one so-called "pure strategy." Other times, you choose another. So it does allow for randomization to try to exploit the weaknesses of an opponent, and to make you appear unpredictable.

Trump is right in the sense that sometimes it does pay to be unpredictable. You can suffer because of that, because you don't develop a reputation that would deter an opponent — let's say an enemy from attacking you. And I think that's a weakness, and, of course, a number of people have pointed out that Trump is all over the place. Therefore, he can't be trusted, even by our allies.

What assumptions are being made about rationality and decision-making?

You assume the players have preferences for different outcomes. A rational strategy would be one that responds to an opponent's, or opponents', possible choices.

An easy case is if you have what's called a "dominant strategy" that’s unconditionally best. Whatever your opponent does, you always have a best choice. But most situations, including in the game of chicken, are such that your best choice depends on what the other player does. So if the other player is not cooperative, then you should cooperate. If the other player is cooperative, then you should exploit that fact and choose a non-cooperative strategy. That's an example of interdependence.

A healthy democracy is based on transparency and clear signals being sent in the "game." But when rules and norms are being bent and broken that signaling breaks down. What happens to the game then?

You might try to construct new rules. I think Trump is not doing a good job of that because he is so inconsistent in a number of different policy areas. So you don't know where he's coming from or where he's going. That creates a problem and prevents his developing a reputation for, let's say, being tough when he has to be tough and being cooperative when the other side is cooperative. I think that's a big problem.

Trump appears to view life, and now his presidency and politics more generally, as a "zero-sum" type of game. What are the limitations of such a way of thinking?

It turns out that in simple 2 x 2 games, in which there are two players each with two strategies, only three of the 78 possible games are zero-sum or total-conflict games. Trump insists on playing this kind of game, in which he thinks he has to win, demolish the opposition. But most games in life are not zero-sum. There's room for negotiation. There's room for cooperation. He usually doesn't see that very well, or he makes concessions, perhaps unnecessarily, to some of the dictators of the world, which is another problem that he has.

Trump is playing a one-iteration, one-move version of politics. But political veterans and others who are institutionalists understand that politics involves multiple rounds of play — building relationships, quid pro quo, horse trading and the like.

That's right. There's a whole theory of repeated play in games, which gives very different outcomes from single-play games. There's a famous game called the Prisoner's Dilemma that has a dominant strategy of non-cooperation. But if you repeat this game again and again, it pays to cooperate, at least on some occasions; because both players do better than not cooperating.

Repeated play does make a difference. I look at it in terms of not just repeating a game, though that's the usual assumption, but in terms of moves, countermoves and counter-countermoves. That's what I call the "theory of moves."

I believe that's the way most of us play games. We don't look just one step ahead. We look at what might happen if I do such and such, how you will respond, and then how might I counter-respond. I think that's a much more sensible way of looking at play in real-life games.

What happens to the game — in this case the game of politics — if you have a player who does not care about its rules or viability long-term? 

I think Trump does care about the game. For him it's all about winning — his winning, and as quickly as possible. It is not a repeated game. He has to kill the opposition, or embarrass it or degrade it. It's not that he's not playing a game. His view of the situation Is zero-sum, total conflict. And he has a psychological need, in my opinion, to come out on top. That's hurt him on several occasions.

In the case of Nancy Pelosi, she's part of the game. She can take him to task when he's playing his shot-run, zero-sum game. She realizes it's not, so she can choose a strategy such as not giving in on the government shutdown, forcing him to give in himself. That, I think, is a good example of his trying to choose a strategy to win by forcing her to back down. But she turned the tables on him, and he ended up losing badly in that particular confrontation.

Gaming out the impeachment battle, if Nancy Pelosi called you for advice what would you tell her?

From Trump's perspective, it would be a total-conflict game, a zero-sum game. The outcomes for him would be that he wins and his opponents lose completely, or vice versa. There are no compromise outcomes.

From Pelosi's perspective, it's not so clear. Does she want to play a win/lose game or are her preferences such that she wants to push for cooperation?

One school of thought says Trump wants to be impeached because that will somehow help him in terms of getting re-elected in 2020. He'll lose the first battle, if he is impeached by the House, but win the second battle in the Senate when the Republicans refuse to convict him. What if Trump and Pelosi and the Democrats are defining "winning" in divergent ways? 

Well, that's a good question, and I don't have a clear answer to that. I think you're right, that there's the impeachment phase in the House and then the Senate phase and possible conviction. In my opinion, Pelosi might think that she's moving toward a position where maybe impeachment is sufficient to embarrass him because she'll get some of his Republican colleagues to probably side with Democrats. But she may not get very many in the House.

Pelosi has to weigh the possibility of getting, let's say, all the Democrats in the House, and a substantial number of Republicans, for impeachment. In my opinion, she's waiting things out to get a clearer idea of how many Republicans she can get to side with her when Trump does something really outrageous.

Can we use game theory to inform our understanding of how a seemingly unpredictable person like Donald Trump will behave in the future?

Game theory does allow for that kind of unpredictability, but that's only in some games. Chicken is actually one in which you can be tough or you can be cooperative. But there's a third, "Mixed Equilibrium," that says sometimes you should choose one strategy and sometimes you should choose the other. And you should be unpredictable about which choice you make.

So game theory is not always as deterministic as some people think it is. It allows for uncertainty. It allows for mixing things up. And, in fact, in the original work by von Neumann and Morgenstern on game theory, the book published in 1944, they show this is optimal in the game of poker.

They show that sometimes players should raise when they don't have high hands, and sometimes they should call when they do have high hands, to keep the other players "in," so to speak.

That's an example of being unpredictable in a well-known game. If you always raise when you have a high hand and call or fold when you have a low hand, people figure that out and can exploit you. But if you are unpredictable and do the opposite of what you would think would be the rational strategy, you actually do better in poker. If you want to use the poker analogy, then it's a game in which unpredictability is a smart choice.

What do we know about the role that signaling and credibility play in international relations?

It makes things very fluid, and makes agreements of any kind difficult. Trump is always quick to say he'll negotiate with anybody, and sometimes he has. But not much has come out of it, or if there's supposedly some kind of agreement it falls apart.

In the case of North Korea, Kim Jong-un didn't do very much. That's a big problem. I don't think Trump is capable of dealing very well with dictators like Kim or Putin because he's such a short-term thinker. Not only is he impulsive and playing this total-conflict game, but he's not thinking more than one or two moves ahead.

Take something like the 1962 Cuban missile crisis. Using the statements of leaders and documentation on the crisis, I reconstructed what the players thought, what their preferences were, and why a cooperative outcome, in this case an agreement, was reached after 13 days. More recently in an unpublished paper, I analyzed the Iran nuclear agreement in 2015 between the U.S., its European allies and Iran. I argue that that was a game in which the cooperative outcome required both sides to think ahead — which Trump later abrogated and which has left us in a mess with Iran.

By Chauncey DeVega

Chauncey DeVega is a senior politics writer for Salon. His essays can also be found at He also hosts a weekly podcast, The Chauncey DeVega Show. Chauncey can be followed on Twitter and Facebook.

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