Information set (game theory)

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.^[1]

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.^[2] 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.^[3]