We prove that a preference relation which is continuous on every straight line has a utility representation if its domain is a convex subset of a finite dimensional vector space. Our condition on the domain of a preference relation is stronger than Eilenberg (1941) and Debreu (1959, 1964), but...

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...