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.

One response to “A Game Theory Application: Is Donald Trump Actually Crazy?”

  1. Certainly plenty of gamesmanship going on here, and indeed it’s *sometimes* good in a negotiation to act more extreme than you actually are…I’ve done so myself.

    But I think idea that we (the US) are reliant on China’s ability to produce goods at lower cost than we can is questionable, at least in the long term. The US was a broadly-prosperous country long before Chinese goods were a big factor in international trade. And the ratio between US production cost and Chinese cost for a particular item isn’t fixed; it’s subject to productivity levels, which in turn are subject to technology, investment, and process-improvement decisions. Shifting of production to the US yields economies of scale for US based producers, and strong incentives for productivity improvement that aren’t there if one can just do the easy thing and offshore the production to some low-cost place.

    Thought experiment: Imagine if Henry Ford had been able to build the Model T in some very-low-wage country…no need to bother with the assembly line and other advanced manufacturing approaches, just hire lots & lots of cheap workers. But given that the product was made in the US, and probably had to be at the time, the productivity improvements did happen.

    Lots of technologies now in development which will considerably reduce the advantage of low-wage countries…see for example the sewing robots discussed in my post here:



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