A note on topological aspects in dynamic games of resource extraction and economic growth theory

We show that right-continuous monotone strategies used in Markov perfect equilibria for economic growth models and related dynamic games can be recognised as members of the Hilbert space of square integrable functions of the state variable. We provide an application of this result to a bequest game and point out that this result also holds for the class of left-continuous monotone functions. The result is fundamental for using the Schauder fixed point theorem. Furthermore, it considerably simplifies the classical approach, where such strategies are represented by non-negative measures on the state space.