Types of games

Game theorists don't classify games to file them away. The classification tells you which solution tool works. You can't backward-induct a game with no order, and you can't trust dominance when information is lopsided.

Seven distinctions do most of the sorting. Each one is a claim a modeller makes about moves, payoffs, or information — and each has everyday tells you can spot without a matrix.

Simultaneous vs. sequential

A simultaneous game is one where every player commits without seeing the others' moves. A sequential game is one where at least one player moves after watching an earlier move. The assertion is about information, not clocks: two firms announcing prices a week apart are still simultaneous if the second firm wrote its number before reading the first. Sequential games get trees; simultaneous games get grids — and a grid can't tell you who reacted to whom, because nobody did.

How to spot it. If the word “then” belongs in the story — “they set prices, THEN you respond” — it's sequential. If nobody can see the other move first, it's simultaneous, even if the clock isn't synced.

In life: price wars and merges run blind; salary talks and market entries run in order.

Zero-sum vs. non-zero-sum

Zero-sum means the payoffs in every cell add to the same constant — whatever one player wins, the other loses. The modeller is asserting that no value is created or destroyed, only moved. Non-zero-sum games have outcomes where both sides gain, both lose, or gain unevenly — which means there is something to cooperate about, or something to squander. Most of the interesting failures in life are non-zero-sum games being played as if they weren't.

How to spot it. Ask whether value is created or just moved. Splitting a fixed pie is zero-sum; growing it is not. Most real negotiations are both at once.

In life: shootouts and poker nights move money around; climate deals and price wars can grow it or burn it.

Cooperative vs. non-cooperative

The distinction is whether agreements bind before play starts. In a cooperative game, players can write enforceable contracts — courts, escrow, coalitions with teeth — so the model studies which coalitions form and how they split what they win. In a non-cooperative game, nothing binds but self-interest, so the model studies what each player does when the only referee is everyone else's incentives. This site's labs are non-cooperative, and so is most of life.

“Non-cooperative” doesn't mean the players fight. It means no external force makes their promises stick. Binding: contracts, escrow, a league that fines no-shows. Not binding: handshakes, New Year's resolutions, most treaties. The same two people with the same stakes are playing different games depending on which list they're on.

How to spot it. The question is whether agreements bind. Contracts with enforcement make the game cooperative; handshakes, treaties, and New Year's resolutions usually don't.

In life: Split bills and group projects are coalition problems wearing casual clothes; the deals worth growing are where cooperation pays.

Symmetric vs. asymmetric

A game is symmetric when swapping the players' chairs changes nothing: both face the same options, and each player's payoffs are a mirror of the other's. Asymmetric games hand players different moves, different payoffs, or both. Symmetry is an assertion the modeller makes so that claims like “both face the same temptation” are literally true rather than rhetorical.

A salary negotiation is what asymmetry looks like: the company can replace you more easily than you can replace it, neither side's payoffs mirror the other's, and the same number means different things to different chairs.

How to spot it. Swap the players' chairs. If the game reads the same, it's symmetric.

In life: merges and arms races are mirror matches; salary talks and used-car lots are not.

Perfect vs. imperfect information

Perfect information means that at every turn, the player about to move can see the entire history of play — nothing hidden, nothing forgotten. Imperfect information means somebody moves in the dark: either the moves are simultaneous or part of the record is concealed. The assertion is about observability, not skill. Perfect-information games can be solved from the ends backward, which is exactly why the entry game below has a solution path: the incumbent sees the entry before choosing its reply.

How to spot it. Can each player, at their turn, see everything that happened before? Chess: yes. Poker: no.

In life: Chess matches and market entries happen in the open; poker nights, shootouts, and auctions happen in the dark.

Complete vs. incomplete information

Complete information means the game itself is common knowledge: the options, the payoffs, and what kind of player sits across from you are known to everyone — and everyone knows that everyone knows. Incomplete information means part of that structure is private. It is not about hidden moves; it is about not knowing what game you are even in — what the other side values, what their real options are, or which kind of opponent you face.

The used car is the canonical case: the seller knows the car, you know the seller knows, and the price has to carry the whole conversation. Signaling is how players try to close the gap — warranties, refunds, and degrees are expensive clues, built so that they are only cheap to give when they are true. The assumptions equilibrium leans on are laid out in The fine print.

How to spot it. Do both players know what game they're in? Incomplete information is about the RULES and PAYOFFS being private, not the moves.

In life: A chess match hides nothing about the game; sealed-bid auctions, used cars, and résumés hide plenty.

These axes stack

Real situations sit at a coordinate on all the axes at once. A sealed-bid auction is simultaneous, imperfect, and usually incomplete — one envelope, hidden values. Chess is sequential, perfect, and complete, and close to zero-sum — one player's advantage is the other's deficit, draws aside. The point of the taxonomy isn't filing. The coordinates tell you which solution tools survive contact with the game — and which ones were never in the toolbox at all.