Open AccessFrom weighted potential game to weighted harmonic game
Author(s) -
Wang Yuanhua,
Liu Ting,
Cheng Daizhan
Publication year - 2017
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2016.1454
Subject(s) - linear subspace , harmonic , mathematics , decomposition , space (punctuation) , game theory , mathematical optimization , pure mathematics , computer science , mathematical economics , physics , ecology , quantum mechanics , biology , operating system
It was shown that the vector space of finite non‐cooperative games can be decomposed into three orthogonal subspaces: the pure potential games (PGs) ( P ), non‐strategic games ( N ), and pure harmonic games ( H ). This study proposes the concept of weighted harmonic game, and shows that in the aforementioned decomposition the P can be replaced by weighted pure PGsP w , and the H can be replaced by WPHGsH w . Then the bases for corresponding orthogonal subspaces are presented, respectively. Finally, certain properties of the new decomposed subspaces are investigated.