Informatiesets

In informatiesets, a concept used in game theory, an information set is a collection of decision nodes in an extensive-form game that belong to the same player and at which the player cannot distinguish which node they are currently at. The information available to the player when making a decision is the same for all nodes in the set, so the player must choose an action without knowing the exact history that led to that point.

Key features include that all nodes in an information set are nodes where the same player must move, and that the available actions at those nodes are the same from the player's perspective. Information sets partition the decision histories of the game for each player, reflecting imperfect information. When a game has perfect recall, the sequence of information sets observed by a player along any history is consistent across possible paths; otherwise, information sets may group histories that share only partial information.

In formal terms, a strategy for a player assigns a probability distribution over actions for each information set, not for each individual node. This allows modeling of uncertainty about the current state or past moves when making decisions.

Information sets are central to analyzing games with imperfect information, such as poker, auctions, or negotiations, where players must act without complete knowledge of the game's exact history. They underpin solution concepts like sequential equilibrium and strategic-form representations of extensive-form games. The Dutch term informatieset is commonly used in textbooks and discussions of these ideas.