Quality & Quantity 37: 91–98, 2003.
© 2003 Kluwer Academic Publishers. Printed in the Netherlands.
A Note on the Structural Notion of Information in
Extensive Form Games
Department of Philosophy, University of Helsinki, P.O. Box 9, 00014 Helsinki, Finland. E-mail:
Abstract. It is argued that the method of representing games by extensive forms and by the associ-
ated partitional information structure calls for a wider and more dynamic deﬁnition of information
set, increasing the overall expressivity of extensive forms of games.
Key words: Extensive form games, partitional information, information set.
1. Structural information in games
When a theory involves some superimposed structure, a natural question to be
asked is how it is being exploited in the theory. Game theory uses a good deal
of structure to capture notions of players’ interaction and players’ knowledge and
information about essential features of games. To this effect, game theorists have
deﬁned players’ information in terms of extensive form games and associated an in-
formational partition with them. Brieﬂy, an extensive form game is a tree structure
specifying how information is transferred in any play of the game from one player
to another. Its purpose is to capture player interaction by visualising which choices
and which moves are made in response to which other choices. More importantly,
however, extensive forms were designed to capture what players know at any part
of the game, and how their information varies as the game goes on.
Shubik (1992: 160) writes that “the development of the notation for the extens-
ive form had a considerable impact on decision theory and psychology. The ability
to represent and analyze different information structures was a breakthrough of the
ﬁrst magnitude”. Alas, the purpose here is to show that the magnitude was perhaps
an order less than customarily thought. There are some fundamental impediments
in the traditional way of representing players’ information by extensive games.
Customarily, extensive forms introduce the notion of informational partition and
deﬁne its basic component of information set such that it assimilates the essentially
different notions of players making moves at the information set and players having