Minimax theorem and Nash equilibrium of symmetric three-players zero-sum game with two strategic variables

Masahiko Hattori (), Atsuhiro Satoh () and Yasuhito Tanaka

MPRA Paper from University Library of Munich, Germany

Abstract: We consider a symmetric three-players zero-sum game with two strategic variables. Three players are Players A, B and C. Two strategic variables are ti and si, i = A;B;C. They are related by invertible functions. Using the minimax theorem by Sion (1958) and the fixed point theorem by Glicksberg (1952) we will show that Nash equilibria in the following four states are equivalent. 1. All players, Players A, B and C choose ti; i = A;B;C, (as their strategic variables). 2. Two players choose ti's, and one player chooses si. 3. One player chooses ti, and two players choose si's. 4. All players, Players A, B and C choose si; i = A;B;C.

Keywords: symmetric three-person zero-sum game; Nash equilibrium; two strategic variables (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
Date: 2018-03-26
New Economics Papers: this item is included in nep-gth and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/85503/1/MPRA_paper_85503.pdf original version (application/pdf)

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:pra:mprapa:85503

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().