A Rough Perspective on Information in Extensive Form Games

Abstract

In game theory imperfect and incomplete information have been intensively addressed. In extensive form games a player faces imperfect information when it cannot identify the decision node it is presently located at. The player is only aware of an information set consisting of more than one node. A player faces incomplete information when it is not aware of, e.g., preferences or payoffs of its opponents. Rough set theory is a prime method addressing missing and contradicting information in decision tables where a set of variables induces a decision. In particular, rough set theory provides a means by which records with identical variable values lead to different, contradicting decisions. To indicate such situations, these records are assigned to the boundaries of all possible decisions. Obviously, both situations, games with imperfect or incomplete information and rough decision tables are similar with respect to their characteristics and challenges regarding a lack of information. Hence, a discussion of their relationship could be mutually beneficial. Therefore, the objective of our paper is to provide a rough set perspective on extensive form games with imperfect and incomplete information.