informationsset

Informationsset is a concept in game theory, particularly in the study of extensive-form games. It refers to a set of decision nodes among which the acting player cannot distinguish the current situation given the information they have. At any node within an information set, it is the same player's turn to move, and the player cannot tell which specific node in the set is the actual one.

Because the player cannot tell the nodes apart, a strategy must prescribe a single action for the entire information set rather than separate actions for each node. In graphical representations of extensive-form games, information sets are typically shown by enclosing the connected nodes with a dashed line or other visible grouping.

Information sets embody imperfect information. If an information set contains more than one node, the player does not know which of those histories occurred. In contrast, in games with perfect information, every information set is a singleton, meaning the player always knows exactly which node is current.

Perfect recall is a related assumption often made in conjunction with information sets. It states that players remember all their past actions and observations, which constrains how information sets can arise and evolve over the course of the game.

A common example is a card game where a player does not observe the opponent’s private cards. After certain moves, the player’s decision may be determined by an information set that groups together multiple possible underlying card configurations.

Informationssets are fundamental to defining strategies and analyzing equilibria in games with uncertainty or hidden information, shaping how players respond when they cannot fully observe the game state.