Information district
Information set (also amount of information ) is a term used in game theory , which serves imperfect information (even imperfect information ) formally by mathematical objects to model .
Examples
Examples of games with imperfect information are most card games , in which an individual player generally does not have comprehensive information about the current game situation, because each player only knows his own cards . An information area then comprises those game situations that are indistinguishable from the point of view of the player who currently has to make a decision. This information area is characterized by the previous course of the game, which in particular includes your own supply of cards.
For example, if player I hides a coin in one hand and lets player II guess which one it is in, the two possible positions of the coin form an information area for player II.
Formal approach
With regard to the formal model of an extensive game , an information district is a set of decision nodes in which a player can find himself in a certain phase of a game without being able to determine with certainty from the previous course of the game which node he is in.
In the graphical representation of an extensive game in the form of a graph , an information area is usually represented by a dashed line through all the nodes of the area or by a cartridge that includes the nodes of the information area.
The concept of the information set goes back to Harold W. Kuhn , who introduced it in 1950.
literature
- HW Kuhn, Extensive games , PNAS, Volume 36 (1950), pp. 570-576.
- HW Kuhn, Extensive games and the problem of information , in: HW Kuhn, AW Tucker (Hrsg.), Contributions to the theory of games , vol. II, Princeton 1953, pp. 193-216, doi : 10.1515 / 9781400881970-012 , ( p. 193 in the Google book search). Reprinted in: H. Kuhn (ed.), Classics in game theory , Princeton 1997, pp. 46-68 ( p. 46 in Google Book Search).
- Jörg Bewersdorff : Luck, Logic and Bluff: Mathematics in Play - Methods, Results and Limits , Wiesbaden 1998; 6th edition 2012, ISBN 978-3-8348-1923-9 , doi : 10.1007 / 978-3-8348-2319-9 , pp. 289 ff.