The paper deals with the question of existence and properties of equilibrated distributions of individual characteristics in an infinite population. General game-theoretic methods are applied and special attention is focused on the case of fitness functions depending only on the distance of an individual characteristic from a reference point and from the mean characteristics. Iterative procedures leading to equilibrated distributions are also considered.
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In this paper, we first discuss some properties of SKC mappings in the context of Busemann spaces and obtain a demiclosedness principle.We then prove the existence and approximation results for SKC mappings in a uniformly convex Busemann space. At the end, we give a numerical example in support of our main result. This example also shows that our iterative process is faster than some well-known iterative processes even for SKC mappings. Our results are certainly more general than many results in the contemporary literature.
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