Our book this week is especially geared towards managers who want to understand why their organization acts the way it does. It’s all a game. Or can be. Because game theory demonstrates the office drama, bad decisions, and emotional tension through simple abstractions. It helps you clearly see where you, and others, have options. Instead of the anxiety-riddled thoughts of what might happen when you enter an argument with a co-worker (What will they say? What will they do?), you can do a simple math and think differently.
If I do x and the other player does y, I will be able to do z and thus achieve N outcome. This is a clearer view of reality. Albeit more simplified.
The clarifying concept in all this is the payoff matrix. It’s the summary of any given set of choices and their expected outcomes. It expands your view to think almost like a stock trader about your choices (which do I invest in?) instead of muddling through. Again, it’s simplified, but developing the ability to do this intuitively is the stuff of mental superpowers. 1
The easy example is The Prisoner’s Dilemma. Stop me if you’ve heard this one.
You and a friend were recently arrested for a crime. You’re sitting in a jail cell, feeling nervous about what’s going to happen next. “No matter what,” you say to your friend, “We’re in this together. I won’t talk if you don’t talk.”
Your friend nods his agreement. You’re in this together. You even shake hands.
A detective comes by and takes you to an interrogation room. He offers you a deal. Squeal on your buddy, spill the beans on all the bad stuff the two of you did, and the warden will reduce your sentence. The same offer is being made to your friend in the next room.
Ha! You think. Too late copper! We already agreed to keep quiet! Blood brothers to the end!
Such solidarity is admirable but it carries a high price. The detective informs you that the sentence for your crime is 10 years if you don’t take the offer. Give up the information and you could walk away with no time in jail. And think about it: your so-called buddy might already be confessing the whole thing in the other room.
Is that true? Would your friend really do that? He agreed to not confess. He didn’t verbally agree—he just nodded his head—but it was still an agreement. You shook hands.
But 10 years is a long time. Maybe your pal is talking. In that case, maybe you should talk.
Oh, but if you both talk, the information isn’t so important anymore so you’ll both get 5 years in the clink.
And if neither of you talk, if you both hold your ground, you’ll only get 6 months of jail time because they’ll have nothing to hold you down.
Like most of life, this is a game of incomplete information. You don’t know what your partner is doing. And since you can’t talk with him and coordinate a response, it’s a non-cooperative game. You’re playing against your friend now, pitted against one another.
Here’s the payoff for the two options you both face:
|The Payoff Matrix||He Talks||He Doesn’t Talk|
||B. You walk, he gets 10 years|
|You Don’t Talk||C. You get 10 years, he walks||D. You each get 6 months|
And here’s the dilemma: if you both just hold to your promise, you’ll be in jail for six months. That’s it. Easy. If either of you crack under the pressure, the other one gets the 10 year stint.
What do you do? Let’s consider from the ethos, pathos, and logos standpoint.
Ethically, keeping your word is important. But since you’re a criminal, you already have a warped sense of ethics so it’s not a reliable gauge.
Emotionally, the shame of ratting a friend out feels terrible but not as terrible as the feeling of 10 years in prison. That’s absolutely terrifying. If you talk, you might walk away. Sure, that might cause you both to talk and that results in more jail time. But it ain’t 10 years. It’s half that.
And what about the logical standpoint? Here’s where game theory shines. Regardless of what your friend does, you can see that your best outcome that avoids time in jail is Option B in the matrix 2. The next best outcome is D. Then A and C.
So again, what do you do? The rational, self-interested player will break their agreement and rat out the partner in a desire to walk. And in an experiment with actual college students, that’s exactly what happened 76% of the time. But when tested against the more-experienced players, some actual prisoners, the rational choice only occurred 44% of the time. Most actual prisoners kept quiet and didn’t rat out their partner.
From a pure probabilistic standpoint, this is the best strategy. The prisoners know this. The mafia knows it, too. Most students don’t have a clue.
In this case, the power of game theory is that it shows the limit of rationality as well as the limit of emotional reasoning. A purely rational, self-interested player will think like a college student. Because it’s irrational, given the obvious upside, to not talk to the cops. But in a fuller picture of all possible outcomes, which is the sort of view you usually gain only by playing the game more than once (a’la gangsters and their long history of criminal activity), you understand what the optimal strategy really is.
In fact, this dilemma and the best strategy against it is so well-understood amongst the usual players (mafia) that it is codified and enshrined as a universal rule known as Omerta.
It’s always fun when street-smarts and book-smarts align. Discovering the best strategy in a given situation without suffering the painful penalties of inexperience is what game theory is all about. So the lesson? Don’t do crime. And in decisions where you have incomplete information, a clear goal, and other players in the field, try working a little game theory. Even just something as simple as writing your payoff matrix will help.
Image of the cast from The Untouchables by Wikimedia Commons