Geometric approaches and bifurcations in the Dichotomous decision model

 Resorting to the Dichotomous decision model, where individuals can make alternative decisions, we study two geometric approaches to construct all possible decisions tiling. Each decision tiling indicates the way the Nash equilibria co-exist and change with the relative decision preferences of the individuals. We find the Nash domains for the pure and mixed strategies and characterize the space of all parameters where the pure Nash equilibria are either cohesive or disparate. We show how the coordinates of the influence matrix together with the total number of individuals affect significantly the occurrence of bifurcations with and without overlaps between the pure strategies.