A Game Theory Application: Is Donald Trump Actually Crazy?

This is a part of my Game Theory Series. I have several equity analyses in the works, but it’s fun to spin the brain in a different direction. Please let me know if you have any questions or comments!

There are mixed views about the President, but he tweets enough content to fuel several blog posts. There are mixed reviews on the political system, like always, and this is not a political blog. This is a finance blog.

So is Donald Trump actually crazy? Or is he just pretending to be crazy so he gets his way? If China really believes some of his trades threats, and that he would be crazy enough to pull out of the trade agreement, would they blink first during trade negotiations? Or do they think he is just acting crazy, and thus wait it out?

Source: Bloomberg

It’s not like the US doesn’t need China. We have a massive trade deficit with them, primarily because we import most of our goods from there. We are reliant on their ability to produce goods at a lower cost than we can.

Source: Bloomberg

But his most recent tweet might shift the scale in a different direction. It definitely sent the stock market on a downward spiral this morning, but only time will tell if this actually plays out. But for now, we must ask ourselves – is Donald Trump crazy?

Source: Twitter

Let’s say that the probability that someone is actually crazy is 5%. The probability that someone is not crazy would then be 95%. So the probability that someone acts crazy, given that they are crazy, is one. Crazy people always act crazy. The probability that someone acts crazy given that they are not crazy is 7% (they are faking crazy), and 93% chance that they act normal, given that they are normal.

  • P(Crazy) = 5%
  • P(Not Crazy) = 95%
  • P(Act Crazy|Crazy) = 100%
  • P(Act Crazy|Not Crazy) = 7%

So here, we have the scenario laid out in game tree form. The probability that someone is crazy and acts crazy is 5%. But the probability that someone who is not actually crazy but is just acting crazy is 6.65%.

We can determine that the probability that someone is acting crazy given that they truly are crazy by taking the percentage of actually crazy people, and dividing it into the total amount of people acting crazy.

Here, there is an 11.65% chance that when challenged, the person will act crazy. We calculate that by adding together the percentage of time that both crazy and not crazy people are acting crazy. So there is a 42.9% chance that the person who is acting crazy is actually crazy.


That’s a little high for me. It’s unlikely that someone will act crazy when challenged (11.65% probability) but we could agree that Trump acts crazy at times, regardless of your political affiliation. But does he fall into the 42.9% of people acting crazy that are actually crazy?

Image result for trump covfefe
Source: Twitter

I’m not sure. Maybe it’s all a negotiation tactic, and maybe it will all pay off. Only time will tell.