Open AccessOn the representation of informational structures in games
Author(s) -
Shravan Luckraz
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022556
Subject(s) - converse , digraph , mathematical economics , set (abstract data type) , game theory , relevance (law) , representation (politics) , sequence (biology) , mathematics , repeated game , extensive form game , computer science , theoretical computer science , discrete mathematics , geometry , politics , biology , political science , law , genetics , programming language
We consider two well-known mathematical representations of informational structures in game theory. The first is based on the set of historical sequences of information encountered in the game while the second is given by the informational digraph of the game. We show that while the latter can always be embedded into the former under some mild technical condition, the converse does not hold in general. We give a necessary and sufficient condition for an informational digraph to be equivalent to a sequence theoretic informational structure and discuss the relevance of this result to game theory.