An information set is part of a dynamic game, made up of a number of nodes in the game tree. An information set is a set of nodes such that the player making the decision at those nodes can't tell which node they are at. Information sets are one of the common parts of games of incomplete information, including games of asymmetric infromation.

For example, suppose that the game includes a move by Nature, who picks either a rainy afternoon or a sunny afternoon. Then a player must decide in the morning whether to bring an umbrella to work or not. Although Nature has (hypothetically) already selected the afternoon's weather, the player doesn't know what was chosen.

There's some requirements for which nodes can be included in an information set:

  1. The same player must be the one making a decision at all the nodes in the information set.
  2. The same choices must be available to the player at each node in the set.
  3. The path to get into one node in the information set must include the same structure as the path to get to any other node in the set.

The third one above is the tricky one, and is sometimes ommitted. Basically, a player should not be able to identify which node they are at by thinking back to the history of how they got there. If the requirement is omitted, it implies that there is something about the game which prevents recall.

If the third requirement is included, the "structure" in question is the structure reletive to the player making the decision in the information set.

For instance, if after Nature decides whether it will be a rainy or sunny afternoon, Nature also decides whether it will be windy or not, but Nature only makes this choice IF it's going to rain. Then, the structure from Nature's point of view is different at the various nodes where the player decides whether to bring an umbrella. But from the player's point of view it could be the same.

On the other hand, suppose that the player gets to decide whether to leave work on time, or wait out the bad weather. One couldn't put the two possible nodes { (decide what to do when player has umbrella), (decide what to do when player does not have umbrella) } into the same information set, because the player themself made one of the decisions which got them to that point.

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