Famous Illustrative Games for Game Theory
This is a list of games which are commonly used in discussion of game theory. Some illustrate a concept particularly well. Some have a "paradox" element to them. For some, experiments have shown that theory makes poor predictions of actual behavior.
(Note these are all for non-cooperative game theory.)
Prisoner's Dilemma and related games
These are games in which there is a dominant strategy which is inefficient. If the players could make a binding agreement, they could all do better. Laboratory experiments often show that people cooperate more than standard theory predicts.
These are games with multiple pure strategy equilibria, and where players would rather successfully be at one of the equilibria (coordinate) than fail to coordinate. Trouble coordinating can arise when the players disagree about which equilibrium is best, or when some equilibria are riskier than others.
Clean zero sum examples
There are two classic games used to illustrate mixed strategy equilibria. Both are zero-sum games, so the formal solution concept goes back to minimax and doesn't technically require the more general Nash equilibrium. But they can still be good illustrations.
Altruism, Trust, Reciprocity, and the like
- Matching pennies (As an aside, I find it endlessly odd that this is used so often as a motivating example. I gather it might have been an actual game people played in some countries at some point, but never once have I seen or heard of people doing this outside the context of academic game theory.)
- Rock-Paper-Scissors (The fact that so many people (Americans at least) know this game intimately makes the use of matching pennies as an example even stranger.)
There are a number of games which are designed to test (either as thought experiments or in actual experiments) various notions of other-regarding preferences.
Industrial organization basics
These are some of the most basic game theory models applied to how businesses should decide to produce & sell when there's competition. They are almost always presented in contrast to each other because they give such different results.
So far only one game here. The centipede game has features in common with prisoner's dilemma type games, in that the commonly predicted outcome is one the players won't like. It is used to illustrate backward induction as a solution concept for dynamic games, and raise questions about whether you can expect players to do so.
Other games, not yet categorized
This list isn't meant to be exhaustive. My idea is that every game described here is one you should know about if you plan to be talking game theory. All the same, if I'm missing something (quite likely), please let me know. I'm particularly trying to recall any canonical games of incomplete information (besides auctions).