Information set (game theory)

These nodes are indistinguishable to the player due to incomplete information about previous actions or the state of the game.

Otherwise, it is the case that some players cannot be sure what the game state is; for instance, not knowing what exactly happened in the past or what should be done right now.

That is, each player does not have complete knowledge of the opponent's information, such as cards that do not appear in a poker game.

Information sets can be easily depicted in game trees to display each player's possible moves typically using dotted lines, circles or even by just labelling the vertices which shows a particular player's options at the current stage of the game as shown in Figure 1.

When chance moves are involved, a vector of strategies can result in the probability distribution of the multiple outcomes of the games that could occur.

Multiple outcomes of games can be created when chance is involved as the moves are likely to be different each time.

The key to solving dynamic game is to calculate each player's information set and make decisions based on their choices at different stages.

The notion of information set was introduced by John von Neumann, motivated by studying the game of Poker.