Game Theory
Six small games, each one a situation people are actually in, written down in as few numbers as it takes. They are played rather than read, and none of them explains itself before you have felt it.
Why a game and not a chapter
A game in this sense is the smallest complete description of a situation: who is deciding, what each of them can do, and what each of them ends up with for every combination of those choices. That is the whole apparatus. Everything else in the subject is a consequence of writing a situation down that carefully.
The trouble is that the consequences are easy to agree with and almost impossible to feel. You can be told that doubt rather than greed is what keeps two hunters apart, agree with it, and learn nothing. Playing one round in which you go hungry because you trusted somebody is a different kind of knowledge, and it is the only kind that changes what you do afterwards. That is what these are for.
Every one of them runs in this page, saves nothing anywhere but your own browser, works without a connection once it has loaded, and ends by saying plainly what it does not show. Where a game states a fact about the world it names the paper it came from and the date it was read.
The games
Where you can both do well, and might not
The Long Game
20 to 30 minutesThe situationThe same two people meet again and again, and each time either can take more by giving nothing.
What it teachesWhy a future changes the arithmetic of the present, why a short rule beats a clever one, and why a rule that answers every observation will answer an accident as though it were a decision.
The Stag Hunt
5 to 10 minutesThe situationTwo hunters can take a stag together and eat well, or a hare alone and eat a little, and whoever waits alone goes hungry.
What it teachesThat the trap is not greed but doubt. There are two equilibria here, and which one a village lives in is settled by what each person believes the other will do.
Where the question is what is acceptable
The Ultimatum
5 to 10 minutesThe situationOne person says how a sum is split and the other can only accept it or destroy it for both of them.
What it teachesThat fairness is a force in real bargaining rather than a soft feeling about it. You will see your own threshold measured and put beside what a purely self interested player would do.
Where everyone is reading everyone else
The Commons
8 to 12 minutesThe situationOne pasture, four households, and an animal that is worth a whole year to whoever owns it and costs the grass to everybody.
What it teachesThat the tragedy is a result about rules rather than about people. You watch the grass go, then live in a rule the four of you agree, and Ostrom's finding is quoted with its source.
The Beauty Contest
5 to 8 minutesThe situationEveryone writes a number from zero to one hundred and whoever is nearest to two thirds of the average takes the purse.
What it teachesHow deep you should reason about other people, which is a fact about the room you are in rather than about mathematics. Keynes on the newspaper competition, quoted with its source.
Where one of you has to lose
Matching Pennies
5 to 10 minutesThe situationPure conflict. She wins when the two coins agree and you win when they differ, and there is nothing else in it.
What it teachesThat sometimes the only unexploitable strategy is to be genuinely random, and that people are not. The opponent learns your habits and the game measures your predictability while you play.
Named, not built
Four more belong in this family and are not written yet. They are listed because a plan nobody can see is not a plan.
The Centipede
A pile of money that doubles every time somebody passes it on, and backward induction says take it at the first move. Almost nobody does.
The Traveler's Dilemma
Two travellers name the value of an identical lost bag and the lower claim is paid to both, with a bonus for undercutting. The equilibrium is the lowest number allowed.
Nash bargaining
Two people divide a gain that exists only if they agree, and what each can walk away to decides most of the split.
Battle of the Sexes
Two people want to be together more than they want their own preference, and there are two ways to manage it and no way to choose between them.
The formal treatment
The evolution of cooperation
The repeated prisoner's dilemma with the payoffs editable, a full round robin tournament between strategies, an evolutionary run in which the winners reproduce, and every source named and dated. Read this one if you would rather check the arithmetic than feel it.
What none of these are
None of these games is evidence about people. Every opponent in them is a short rule written by hand, and where a rule was chosen to make a point the game says so on its last screen. The experimental findings that are quoted are quoted from the papers and linked to them, and nothing that could not be verified was used.
A model is a claim about which parts of a situation matter. Each of these pages ends with the parts it left out, because that list is usually more useful than the model itself.