Information set (game theory)

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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 so far. 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.