The Mysteries of Obama: A Game-Theoretic Analysis

President Obama has been on a losing streak in the international arena, claiming as victories against Russia, Iran, and Syria what any sensible observer would see as major defeats. Yet he seems to run rings around Congressional Republicans, who have approved a budget deal that funds Planned Parenthood, expanded admission of refugees, and even the Office Of Civil Rights’ assault on due process—not to mention the President’s war on the suburbs, also known as the Affirmatively Furthering Fair Housing rule. What’s going on? If Putin, Assad, and the mullahs have his number, why is the Congressional majority incapable of winning even minor battles?

I want to suggest an explanation. Many people have noted Obama’s strange foreign policy: punish your friends and reward your enemies. Take that as a strategy for playing iterated prisoners’ dilemmas, and the above results start to make sense. A common and highly successful strategy for iterated prisoners’ dilemmas is Tit-for-Tat: start by cooperating, and then do what the other player did on the last turn. Obama’s strategy is basically the reverse of that: start by cooperating, and then do the opposite of what the other player did on the last turn.

See what happens if we play Obama against Tit-for-Tat (where C means cooperate, and D means defect):

Turn 1 2 3 4 5 6 7 8 9 10
Obama C D D C C D D C C D
Tit-for-Tat C C D D C C D D C C

This four-round cycle continues. If we have a stable payoff matrix like this,

Cooperate Defect
Cooperate 3, 3 0, 5
Defect 5, 0 1, 1

then Obama and Tit-for-Tat each average 2.25 points per turn—not terrible, but worse than they could have done by cooperating consistently.

The more forgiving the opposing strategy is, the better Obama does, and the worse the opponent does. Here’s Obama vs. Tit-for-Two-Tats:

Turn 1 2 3 4 5 6 7 8 9 10
Obama C D D D C C D D D C
Tit-for-Two-Tats C C C D D C C C D D

Here there is a five-round cycle. Obama averages 2.8 per turn, while Tit-for-Two-Tats averages 1.8. Tit-for-Three-Tats would do even worse, producing a six-round cycle that yielded it an average of 1.5 per turn. (Obama meanwhile would earn almost 3.2 per turns.) The extreme case, a strategy that always cooperates, would after the first turn get no points at all, while Obama would get 5 every time.

Moral for Republicans: the more cooperative and forgiving you are, the better Obama does, and the worse you do.

Now see what happens if Obama goes up against a tough guy who always defects. Call that strategy Putin. It’s a disaster for Obama:

Turn 1 2 3 4 5 6 7 8 9 10
Obama C C C C C C C C C C
Putin D D D D D D D D D D

Putin gets 5 every time, and Obama gets nothing. Something similar happens if Obama goes up against a strategy that cooperates until the opponent defects, after which it invariably defects. (Fool me once….) Obama defects in the second round, and the opponent retaliates by defecting ever after—while Obama in response keeps trying to cooperate, in effect trying to atone for his earlier sin.

Moral for Obama: Apology tours, red lines, executive agreements, treaties, etc., etc., don’t work against an implacable foe. And the world is full of them.

2 thoughts on “The Mysteries of Obama: A Game-Theoretic Analysis

  1. It is easy to see that the strategy has the result you claim. That’s perfectly clear.

    The question is why one would adopt such an evolutionarily unstable strategy. I can think of two reasons:

    (A) A cowardly bully reacts to how people act. When someone is nice and cooperative, ruthlessly exploit them. When someone is threatening, cower and give them whatever they want.

    (B) It depends on the other player, not on their behavior. Those who cooperate with The West are evil and should be ruthlessly exploited as punishment, while those who oppose The West are virtuous and authentic, so they should be rewarded with whatever they want.

    Any reaction?

  2. Great question, and I have some sympathy with both responses. (A) is, I think, a quick summary of the Chicago way—bully those you can bully, and kowtow to those more powerful than you. But (B) does seem to reflect Obama’s worldview, as reflected in his Cairo speech, his apology tour, his prayer breakfast speech, and his general policies toward traditional allies and enemies. Maybe the combination explains why he has been unable to learn from his repeated defeats.

    One way to distinguish these options would be to ask about expectations. If (A) holds, there’s no expectation of change; exploit the chump and be exploited by the greater bully. If (B) holds, there might be; maybe he wants to align us with Russia and Iran against Israel and Western Europe. Call that (B1). But (B) is also consistent with thinking that his job is to engineer America’s defeat at the hands of its enemies because he sympathizes with the enemies and not with us. In that case, he’s playing the game trying to lose; his own personal payoffs are those of the enemy, not of his own side. Call that (B2). I think there’s some evidence for each of the above.

    I don’t think Obama is particularly smart, so I think (A), (B1), and (B2) may all be playing some role in his mind. I think on some level he did expect some kind of rapprochement with Russia and Iran; on another level, he doesn’t care, because a defeat for the U.S. is a win for him. Sometimes I think that he’s actually been brilliant in achieving his goals, but it doesn’t take that much brilliance to screw things up. If your goal is to lose, then it’s usually easy to accomplish your goal.

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