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Random collision models in oriented graphs

Published online by Cambridge University Press:  14 July 2016

Yoshiaki Itoh
Yoshiaki Itoh*
Affiliation:
Institute of Statistical Mathematics, Tokyo
*
∗Postal address: The Institute of Statistical Mathematics, 4–6–7 Minami-Azabu Minato-Ku, Tokyo, Japan.
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Abstract

We investigate a random collision model for competition between types of individuals in a population. There are dominance relations defined for each pair of types such that if two individuals of different types collide then after the collision both are of the dominant type. These dominance relations are represented by an oriented graph, called a tournament. It is shown that tournaments having a particular form are relatively stable, while other tournaments are relatively unstable. A measure of the stability of the stable tournaments is given in the main theorem.

Keywords

RANDOM COLLISIONORIENTED GRAPHSTOURNAMENTSCOMPETING SPECIESMARTINGALESASYMPTOTIC PROBABILITY OF COEXISTENCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 1 , March 1979 , pp. 36 - 44
Copyright
Copyright © Applied Probability Trust 1979 

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