Sequential game

In game theory, a sequential game is defined as a game where one player selects their action before others, and subsequent players are informed of that choice before making their own decisions.^[1] This turn-based structure, governed by a time axis, distinguishes sequential games from simultaneous games, where players act without knowledge of others’ choices and outcomes are depicted in payoff matrices (e.g., rock-paper-scissors).

Sequential games are a type of dynamic game, a broader category where decisions occur over time (e.g., differential games), but they specifically emphasize a clear order of moves with known prior actions. Because later players know what earlier players did, the order of moves shapes strategy through information rather than timing alone. Sequential games are typically represented using decision trees, which map out all possible sequences of play, unlike the static matrices of simultaneous games. Examples include chess, infinite chess, backgammon, tic-tac-toe, and Go, with decision trees varying in complexity—from the compact tree of tic-tac-toe to the vast, unmappable tree of chess.^[2]