In game theory, an information set is the basis for decision making in a game, which includes the actions available to players and the potential outcomes of each action. It consists of a collection of decision nodes that a player cannot distinguish between when making a move, due to incomplete information about previous actions or the current state of the game. In other words, when a player's turn comes, they may be uncertain about which exact node in the game tree they are currently at, and the information set represents all the possibilities they must consider. Information sets are a fundamental concept particularly important in games with imperfect information.

In games with perfect information (such as chess or Go), every information set contains exactly one decision node, as each player can observe all previous moves and knows the exact game state. However, in games with imperfect information—such as most card games like poker or bridge—information sets may contain multiple nodes, reflecting the player's uncertainty about the true state of the game. This uncertainty fundamentally changes how players must reason about optimal strategies.

The concept of information set was introduced by John von Neumann, motivated by his study of poker, and is now essential to the analysis of sequential games and the development of solution concepts such as subgame perfect equilibrium and perfect Bayesian equilibrium.

Information sets are primarily used in extensive form representations of games and are typically depicted in game trees. A game tree shows all possible paths from the start of a game to its various endings, with branches representing the choices available to players at each decision point.

For games with imperfect information, the challenge lies in representing situations where a player cannot determine their exact position in the game. For example, in a card game, a player knows their own cards but not their opponent's cards, creating uncertainty about the true game state. This uncertainty is modeled using information sets.

Information sets are typically represented in game trees using dotted lines connecting indistinguishable nodes, ovals encompassing multiple nodes, or similar notations indicating that a player cannot tell which of several positions they are actually in. This visual representation helps analyze how uncertainty affects optimal play.

An information set in an extensive form game must satisfy the following properties:

The structure of information sets profoundly affects strategic reasoning. When a player faces an information set with multiple nodes, they must formulate strategies that are optimal across all possible game states represented by that information set.