In game theory, an information set is a set that, for a particular player, establishes all the possible moves that could have taken place in the game so far, given what that player has observed. If the game has perfect information, every information set contains only one member, namely the point actually reached at that stage of the game. Otherwise, it is the case that some players cannot be sure exactly what has taken place so far in the game and what their position is.

More specifically, in the extensive form, an information set is a set of decision nodes such that:

1. Every node in the set belongs to one player.
2. When play reaches the information set, the player with the move cannot differentiate between nodes within the information set, i.e. if the information set contains more than one node, the player to whom that set belongs does not know which node in the set has been reached.

[edit] Example

At the right are two versions of the battle of the sexes game, shown in extensive form.

The first game is simply sequential-when player 2 has the chance to move, he or she is aware of whether player 1 has chosen O(pera) or F(ootball).

The second game is also sequential, but the dotted line shows player 2's information set. This is the common way to show that when player 2 moves, he or she is not aware of what player 1 did.

This difference also leads to different predictions for the two games. In the first game, player 1 has the upper hand. They know that they can choose O(pera) safely because once player 2 knows that player 1 has chosen opera, player 2 would rather go along for o(pera) and get 2 than choose f(ootball) and get 0. Formally, that's applying subgame perfection to solve the game.

In the second game, player 2 can't observe what player 1 did, so it might as well be a simultaneous game. So subgame perfection doesn't get us anything that Nash equilibrium can't get us, and we have the standard 3 possible equilibria:

1. Both choose opera;
2. both choose football;
3. or both use a mixed strategy, with player 1 choosing O(pera) 3/5 of the time, and player 2 choosing f(ootball) 3/5 of the time.

[edit] See also

• Self-confirming equilibrium

v • d • e Topics in game theory Definitions Normal-form game · Extensive-form game · Cooperative game · Information set · Preference Equilibrium concepts Nash equilibrium · Subgame perfection · Bayesian-Nash · Perfect Bayesian · Trembling hand · Proper equilibrium · Epsilon-equilibrium · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy · Risk dominance · Pareto efficiency · Quantal response equilibrium · Self-confirming equilibrium Strategies Dominant strategies · Pure strategy · Mixed strategy · Tit for tat · Grim trigger · Collusion · Backward induction Classes of games Symmetric game · Perfect information · Simultaneous game · Sequential game · Repeated game · Signaling game · Cheap talk · Zero-sum game · Mechanism design · Bargaining problem · Stochastic game · Large poisson game · Nontransitive game · Global games Games Prisoner's dilemma · Traveler's dilemma · Coordination game · Chicken · Centipede game · Volunteer's dilemma · Dollar auction · Battle of the sexes · Stag hunt · Matching pennies · Ultimatum game · Minority game · Rock-paper-scissors · Pirate game · Dictator game · Public goods game · Blotto games · War of attrition · El Farol Bar problem · Cake cutting · Cournot game · Deadlock · Diner's dilemma · Guess 2/3 of the average · Kuhn poker · Nash bargaining game · Screening game · Trust game · Princess and monster game Theorems Minimax theorem · Purification theorem · Folk theorem · Revelation principle · Arrow's impossibility theorem See also Tragedy of the commons · All-pay auction · List of games in game theory