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Game theory is a bad name for a useful thing.
It is the study of choices where the result depends on what somebody else chooses at the same time.
Rent negotiations. Two shops setting prices. Who does the washing up. Anything where the right move depends on their move.
Two people are arrested and held apart. Each is offered the same deal.
Stay quiet and, if the other stays quiet too, you both get a short sentence. Talk while the other stays quiet, and you walk free while they take a long one. Both talk, and you both get a middling sentence.
Neither knows what the other will do.
You are one of them. What should you do?
Both of them reason perfectly, and both end up worse off than if they had both stayed quiet.
Nobody was stupid. Nobody was betrayed by a fool. The structure of the situation did that, not the people in it.
That is the whole point of the exercise, and it is why it is famous.
Talking was better whatever the other person did. A move like that is called dominant, and it is rare and very valuable.
When you have one, you do not need to predict anybody. Most situations do not offer one, which is why most situations are hard.
The both-talk result has a property worth naming. Neither person can improve by changing their mind alone.
Mathematicians call that an equilibrium. It means stable, not good.
Most of the bad arrangements people are trapped in are exactly this: nobody can fix it by moving first.
Which of these has the same shape as the prisoners' problem?
Tap an item, then a bucket
Some situations have no conflict at all, only the need to agree.
Which side of the road. Which messaging app the family uses. What time the meeting is.
Nobody gains by defecting. The only difficulty is landing on the same answer, which is why these get solved by law, habit or whoever speaks first.
What changes if the two prisoners will face each other again next week, and the week after?
In 1980 a political scientist invited experts to submit computer programs to play this game against each other, over and over.
Game theorists, economists, psychologists and mathematicians entered. Some strategies were long and cunning.
The winner was the shortest program submitted.
It cooperated on the first move. After that it simply copied whatever the other side did last time.
That is the entire strategy. It was entered by a mathematician and psychologist, and it won twice, against fields that had seen it win once.
Four properties get named for it, and they read like advice about people.
It was never the first to defect. It hit back immediately, so it could not be farmed. It forgave at once, so a single mistake did not start a war. And it was easy to understand, so the other side could see cooperating was safe.
Match each property to what happens without it.
Tap one side, then its match
Repetition only works if the other side expects to meet you again, or to meet somebody who has heard about you.
That is what a reference is. That is what a review is. A trade with strangers turns into a repeated game the moment somebody keeps records.
Sometimes the winning move is to remove your own options, in public.
A shop that advertises no haggling cannot be haggled with. A negotiator who says the board will not approve above this number has made a threat that no longer depends on their nerve.
Being unable to give in is a strange kind of strength.
Two people are splitting furniture after sharing a flat. What is the most expensive assumption they can make?
The same shape with hundreds of players is harder, because you cannot copy anyone's last move.
A shared field, a fishery, a road at rush hour. Each person taking a little more is individually sensible and collectively ruinous.
These get solved by rules, quotas and monitoring, not by goodwill.
It is a model, and models leave things out on purpose.
It assumes people know what they want and can work out the consequences. Real people are angry, tired, loyal, and often willing to lose in order to be fair.
The assumption is not a flaw. It is a starting point you correct from.
You will not sit down and draw a grid in real life. You do not need to.
Ask what the other side gets from each of your options. And ask whether this happens once, or again.
Those two questions are most of the value, and almost nobody in the room will have asked either.