A Note on Nash Equilibrium andFixed Point Theorems

Hannu Salonen and Mitri Kitti
Additional contact information
Mitri Kitti: University of Turku

No 131, Discussion Papers from Aboa Centre for Economics

Abstract: We give a proof of the existence of a Nash equilibrium forn-personnormal form games when each player’s utility function is continuousw.r.t. strategy profiles, and concave and differentiable w.r.t. his ownstrategy. The proof uses only elementary mathematical tools such asmathematical induction. We show that this equilibrium existence re-sult is sufficiently general to imply the Brouwer Fixed Point Theorem.The Kakutani Fixed Point Theorem is obtained as a corollary by usingstandard techniques.

Keywords: Nash equilibrium; fixed-point theorem (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
Pages: 10
Date: 2019-12
New Economics Papers: this item is included in nep-gth, nep-mic, nep-ore and nep-upt
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://ace-economics.fi/kuvat/dp131.pdf (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:tkk:dpaper:dp131

Access Statistics for this paper

More papers in Discussion Papers from Aboa Centre for Economics Contact information at EDIRC.
Bibliographic data for series maintained by Susmita Baulia ().