We study what topological assumptions should be added to the acyclicity of individual best response improvements in order to ensure the existence of a (pure strategy) Nash equilibrium as well as the possibility to reach a Nash equilibrium in the limit of a best response improvement path.

The UEFA Champions League is an annual Pan-European football competition that takes place parallel to the domestic league competitions. The participation in the Champions League secures the teams large payments, which have steadily increased over the last decade. This paper develops a general...