Abstract: We discuss the policy and dynamic implications of nonlinear convex mechanisms in deterministic models of endogenous growing economies. In the first part of this presentation, we discuss the policy implications of global nonlinear phenomena in a representative agent economy facing convex risk premium and investment adjustment costs. Departing from the hypothesis that local analysis of economic systems focus the definition of policy on short run outcomes. We propose that in order to have a clearer perspective on a long run scenario, we have to focus in global analysis instead. In the second part of this presentation, we put forward sufficient conditions for the existence of differential adaptive belief systems (ABS), in games where players face a positive probability of switching between incomplete and complete information strategies. We show that optimal evolutionary outcomes can be efficiently determined assuming a repeated optimal stooping regret matching mechanism. We conclude this presentation with a discussion on the existence of feasible ABS scenarios in a differential game where asymmetric players face coupled endogenous risk premium dynamics.