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An algorithm for computing explicit expressions for orthogonal projections onto finite-game subspaces
KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0001-9940-5929
2018 (English)In: 2018 IEEE Conference on Decision and Control (CDC), Institute of Electrical and Electronics Engineers (IEEE), 2018, p. 3196-3202, article id 8619421Conference paper, Published paper (Refereed)
Abstract [en]

The space of finite games can be decomposed into three orthogonal subspaces, which are the subspaces of pure potential games, nonstrategic games, and pure harmonic games as shown in a paper by Candogan et al. [2]. This decomposition provides a systematic characterization for the space of finite games. Explicit expressions for the orthogonal projections onto the subspaces are helpful in analyzing general properties of finite games in the subspaces and the relationships of finite games in different subspaces. In the work by Candogan et al., for the two-player case, explicit expressions for the orthogonal projections onto the subspaces are given. In the current paper, we give an algorithm for computing explicit expressions for the n-player case by developing our framework in the semitensor product of matrices and the group inverses of matrices. Specifically, using the algorithm, once we know the number of players, no matter whether we know their number of strategies or their payoff functions, we can obtain explicit expressions for the orthogonal projections. These projections can then be used to analyse the dynamical behaviors of games belonging to these subspaces.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2018. p. 3196-3202, article id 8619421
Series
IEEE Conference on Decision and Control, ISSN 0743-1546
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:kth:diva-245110DOI: 10.1109/CDC.2018.8619421ISI: 000458114803002Scopus ID: 2-s2.0-85062193826ISBN: 978-1-5386-1395-5 (print)OAI: oai:DiVA.org:kth-245110DiVA, id: diva2:1294110
Conference
57th IEEE Conference on Decision and Control, CDC 2018; Centre of the Fontainebleau in Miami Beach Miami; United States; 17 December 2018 through 19 December 2018
Note

QC 20190306

Available from: 2019-03-06 Created: 2019-03-06 Last updated: 2019-11-14Bibliographically approved

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Zhang, Kuize

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