Sequential game
Sequential game
thumb|[[chess is an example of a 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. 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.
Representation and analysis Decision trees, the extensive form of sequential games, provide a detailed framework for understanding how a game unfolds. They outline the order of players’ actions, the frequency of decisions, and the information available at each decision point, with payoffs assigned to terminal nodes. This representation was introduced by john-von-neumann and refined by Harold W. Kuhn between 1910 and 1930.
Games can also be categorized by their outcomes: a game is strictly determined if rational players arrive at one clear payoff using fixed, non-random strategies (known as "pure strategies"), or simply determined if the single rational payoff requires players to mix their choices randomly (using "mixed strategies").