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1 results

  • Random collision models in oriented graphs

  • Yoshiaki Itoh
  • Journal:
    Journal of Applied Probability / Volume 16 / Issue 1 / March 1979
    Published online by Cambridge University Press:
    14 July 2016, pp. 36-44
    Print publication:
    March 1979

  • 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.