Strictly copositive matrices and ESS's
type: Item
instance of: scholarly article
title: Strictly copositive matrices and ESS's
zbMATH Open document ID: 0667.15012
DOI: 10.1007/BF01190275
author: Helmut Länger
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: Let A be some real \(n\times n\)-matrix and let \(x^ TAy\) denote the corresponding bilinear form \((x,y\in {\mathbb{R}}^ n)\). A is called strictly copositive if \(x^ TAx>0\) for all \(x\in [0,\infty)^ n\setminus \{(0,...,0)\}\). Put \(S_ n:=\{(x_ 1,...,x_ n)\in {\mathbb{R}}^ n| \quad x_ 1,...,x_ n\geq 0;\) \(x_ 1+...+x_ n=1\}\). \(p\in S_ n\) is called an evolutionarily stable strategy (ESS) (with respect to A) if \((p-x)^ TAp\geq 0\) for all \(x\in S_ n\) and if in addition \((p-x)^ TAx>0\) for all \(x\in S_ n\setminus \{p\}\) for which \((p-x)^ TAp=0\). A simple proof of an already known result concerning the characterization of strictly copositive matrices of dimension 3 [cf. \textit{K. P. Hadeler}, Linear Algebra Appl. 49, 79-89 (1983; Zbl 0506.15016)] is given and it is shown how knowing if a certain matrix is strictly copositive helps in deciding if some element of \(S_ n\) of the form (0,...,0),1,0,...,0) is an ESS.
reviewed by: Helmut Länger
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A63
Mathematics Subject Classification ID: 91A99
zbMATH DE Number: 4091666
zbMATH Keywords: evolutionary game
zbMATH Keywords: bilinear form
zbMATH Keywords: evolutionarily stable strategy
zbMATH Keywords: strictly copositive matrices
MaRDI profile type: Publication
cites work: Q3943082
cites work: On copositive matrices
cites work: Q3992992
cites work: Q3040961
cites work: The Logic of Animal Conflict
full work available at URL: https://doi.org/10.1007/bf01190275
OpenAlex ID: W2031200514
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description: scientific article; zbMATH DE number 4091666