Game theory is the study of how to choose the best move and to get the most stuff when other players are trying to take it. They should teach it after counting but before the alphabet. Too many people make decisions based on gut instinct, invisible sorcerers, Jenny McCarthy, and other things that mean "Hey, even I don't understand why I'm such a stupid asshole." I've studied game theory, because I will do anything that makes my resume look more like Captain N's, and because I count choosing the craziest Magic: The Gathering cards as a career skill. Now my best move for making rent is telling you about the basics.
#5. Prisoner's Dilemma
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Berto and Robert have been arrested for robbing a bank and failing to correctly use a stolen getaway car. The police can't prove they robbed the bank, but found them in the car. (They failed pretty hard.) They're separated and offered a deal: rat out the other guy and go free while the other serves 10 years. But if they both rat each other out, they'll both do seven years. If no one says anything, they'll both do two for stealing the car.
And for using GTA as a driving instructor.
Each prisoner is a player, and their rewards can be written as (what they get, what the other person gets). For example, if I kick you in the crotch, my reward matrix is (I get slapstick victory, you get awful crotch pain). Because each prisoner has two choices, we can represent the results in a two-by-two grid.
So if Berto is silent but Robert rats him out, Berto serves 10 years while Robert serves none.
Real-World Application: Jerk Detection
This is where we see game theory's primary use: identifying total sociopaths. Real game theory is a powerful analytical tool, but amateur game theory is often a red flag planted in an asshole. People who value arithmetic over empathy say you're better as a rat because it leads to a shorter prison term no matter what the other player does. Technically true, if you're a short-sighted asshole who values numbers over human lives. Which is why game theory is so popular in finance. You couldn't be more of a jerk without a red shell.
The real problem with the prisoner's dilemma is that it ignores data. Like how you might not be a psychotic asshole who'd throw someone under the bus the moment a matrix told you to. Or how you'll go free only to be stabbed by your partner's angry friends, family, or some random thug he just promised your half of the money to because he won't see it for 10 years.
"We, uh, weren't very good at robbing the bank, either."
Worst of all, everyone in the prisoner's dilemma suffers from Zombie Movie Syndrome: they act like they've never heard of the prisoner's dilemma. The best move is to keep silent, then enjoy the money with a much closer friend after two years of anticipating the sweetest daiquiris of all time.
The daiquiri dilemma is "Should I have another daiquiri?" versus "Why don't I already have another daiquiri?"
#4. Strictly Dominant Strategy
A strictly dominant strategy isn't something that costs extra at Mister De Sade's Vigorous Exercise Emporium.
The last time we used a whip in game theory we killed Dracula.
It's a move that gives the best rewards no matter what your opponent does. No matter what happens, you did the right thing. That's why people like the prisoner's dilemma so much: betrayal leads to a "better" result no matter what the other person does. Well, that's one of the reasons. The other reason is that it's Chapter 1, Section 1 of every game theory textbook and ignores enough of reality to make things look super simple.
Most games we play don't have strictly dominant strategies, because they'd be terrible games. You'd only ever do that one thing. In Rock-Paper-Scissors, there is no dominant strategy. But if you were playing against someone wearing oven gloves, so they can only make rock or paper, now you have a strictly dominant strategy: paper. Your paper will beat their rock or draw with their paper, and you can't lose, because they can't make scissors. Now that you have a strictly dominant strategy, you'd be a fool to try anything else.
Be warned that "rolling pin" beats everything.
Real-World Application: Tolerance
Another example of strictly dominant strategies would be looking at the rewards of being homophobic versus not being a hateful asshole.
As you can see, it is strictly dominantly better to not be homophobic. Which is a phrasing we're sure the target audience will love.
#3. Battle of the Sexes
Games are more interesting when they don't have a strictly dominant strategy. For example, the battle of the sexes. Anjali and Borislav are going on a date but can't decide between ballet and boxing. Anjali enjoys boxing because she's interested in commercial blood sacrifice, destroying the minds of athletes for baying crowds who claim to be civilized because they used a credit card to pay for someone else's brain damage.
Borislav wants to watch ballet, because he understands that ballet dancers go through more physical trauma, extreme training, and moments of knowing that a single physical injury could end everything than SAS squads infiltrating nuclear launch facilities. Ballet dancers are some of the ultimate athletes on Earth. A ballet dancer could kick your head in, but wouldn't, because your entire face isn't worth as much to the world as the curve of their instep.
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He can kick your ass while showing you his.
They both prefer their own event but won't enjoy anything without their partner, so their rewards are: a large value for doing something they like, a small value for just being with the other person, and zero for being alone.
The only winning move is not to ... wait, wrong game.
Some people propose bull-headed brinkmanship: if you make it absolutely clear that you're doing your thing no matter what, the other person has to match your choice or lose everything. Like I said, simplified game theory is an excellent asshole detector.
Real-World Application: Avoid the Brink
Of course, that strategy has significant problems. The first is that if you refer to your dates as the "battle of the sexes," then jeez, it's not working. Break up so you can both go find someone you like. But the second problem is that in this scenario they're so desperately insecure that they can't do that. They can't enjoy an ultimate expression of the human body's ability, or the destruction of that ability, without their partner clinging on their arm. That kind of desperation is how you end up rationalizing a partner's sweet habit of skinning road-kill.
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"The swearing as she flays their skulls is adorable!"
The real winning strategy is for each to do what they want and then meet for a drink afterward. Or the next day, when they're not busy. Or they take turns, alternating boxing and ballet, before revolutionizing the world of physical entertainment by inventing thunder-ballet-boxing.
"Thunder" appears automatically when a sport gets awesome enough.