Persistent ideologies in an evolutionary setting

We analyse finite two player games in which agents maximize given arbitrary private payoffs which we call ideologies. We define an equilibrium concept and prove existence. Based on this setup, a monotone evolutionary dynamic governs the distribution of ideologies within the population. For any finite 2 player normal form game we show that there is an open set of ideologies being not equivalent to the objective payoffs that is not selected against by evolutionary monotonic dynamics. If the game has a strict equilibrium set, we show stability of non-equivalent ideologies. We illustrate these results for generic 2 x 2-games.