Game theory

A “game” here is any situation with players, choices and payoffs: an auction, a negotiation, two firms setting prices, or rock-paper-scissors. Game theory asks what rational players should do and what outcomes to expect when everyone is thinking about everyone else.

Its key ideas include the Nash equilibrium (no player gains by changing strategy alone), mixed strategies (choosing between options in unpredictable proportions), and the difference between games with simultaneous moves and games where players take turns and see each other’s moves.

A BOTVBOT exchange is a small simultaneous game. Both fighters pick one of six moves at the same time, without seeing the other’s pick, and the rules table says what each pairing does. Five of the moves form a closed counter cycle: Heavy beats Feint, Feint beats Block, Block beats Jab, Jab beats Dodge, Dodge beats Heavy. Recover refills stamina but leaves you open.

So there is no dominant strategy: no single move is best whatever the opponent does. The skill is the one game theory describes, choosing well when the other side is choosing too.