Isotone recursive methods: the case of homogeneous agents

Over the last decade, isotone recursive methods have provided unified catalog of results on existence, characterization, and computation of Markovian Equilibrium Decision Processes (MEDPs) in infinite horizon economies where the second welfare theorem fails. Such economies include models with production nonconvexities, taxes, valued fiat money, models with monopolistic competition, behavioral heterogeneity, and incomplete markets. In this paper, we survey this emerging class of methods. Our methods use a qualitative approach to economic equilibria first introduced in the work in operations research by Veinott and Topkis. As the methods emphasize the role of order, they are amenable for obtaining conditions for monotone comparison theorems on the space of economies. We are also able to describe monotone iterative procedures that provide the needed foundations for a theory of numerical solutions for MEDPs and stationary Markov equilibrium (SME). One interesting additional result of independent interest is we construct sufficient conditions for the existence of a new class of envelope theorems for nonconcave programming problems.