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Random collision models in oriented graphs

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.