Characteristic sets and characteristic numbers of matrix two-person games

D. T. K. Huyen (), J.-C. Yao () and N. D. Yen ()
Additional contact information
D. T. K. Huyen: Hanoi Pedagogical University 2
J.-C. Yao: China Medical University
N. D. Yen: Vietnam Academy of Science and Technology

Journal of Global Optimization, 2024, vol. 90, issue 1, No 8, 217-241

Abstract: Abstract Focusing on the extreme points of the solution sets of matrix two-person games, we propose the notions of characteristic sets and characteristic numbers. The characteristic sets (resp., the characteristic numbers) are the sets (resp., the numbers) of the extreme points of the solution set of the game and the optimal solution sets of the players. These concepts allow us to measure the complexity of the game. The larger the characteristic numbers, the more complex the game is. Among other things, we obtain upper bounds for the characteristic numbers and give a novel geometric construction. By the construction, we get useful descriptions of the optimal strategy set of each player of a game given by any nonsingular square matrix. Namely, the investigation of the geometry the just-mentioned sets reduces to computing or studying certain simpler sets. We also formulate several open problems.

Keywords: Matrix two-person game; Mixed strategy; Linear program; Extreme point; Characteristic set; Characteristic number; Upper bound; 91A05; 91A10; 90C05 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10898-024-01394-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:90:y:2024:i:1:d:10.1007_s10898-024-01394-0

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-024-01394-0

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().