A New Existence and Uniqueness Theorem for Continuous Games

Seamus Hogan

Working Papers in Economics from University of Canterbury, Department of Economics and Finance

Abstract: This paper derives a general sufficient condition for existence and uniqueness in continuous games using a variant of the contraction mapping theorem applied to mapping from a subset of the real line on to itself. We first prove this contraction mapping variant, and then show how the existence of a unique equilibrium in the general game can be shown by proving the existence of a unique equilibrium in an iterative sequence of games involving such R-to-R mappings. Finally, we show how a general condition for this to occur is that a matrix derived from the Jacobean matrix of best-response functions be have positive leading principal minors, and how this condition generalises some existing uniqueness theorems for particular games.

Keywords: Existence; Uniqueness; Continuous Games; Contraction Mapping Theorem (search for similar items in EconPapers)
JEL-codes: C62 C72 D43 (search for similar items in EconPapers)
Pages: 28 pages
Date: 2010-10-01
New Economics Papers: this item is included in nep-gth
References: Add references at CitEc
Citations:

Downloads: (external link)
https://repec.canterbury.ac.nz/cbt/econwp/1059.pdf (application/pdf)

Related works:
Journal Article: A New Existence and Uniqueness Theorem for Continuous Games (2011)
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:cbt:econwp:10/59

Access Statistics for this paper

More papers in Working Papers in Economics from University of Canterbury, Department of Economics and Finance Private Bag 4800, Christchurch, New Zealand. Contact information at EDIRC.
Bibliographic data for series maintained by Albert Yee (albert.yee@canterbury.ac.nz).