Markovian Equilibrium in Infinite Horizon Economies with Incomplete Markets and Public Policy

We develop an isotone recursive approach to the problem of existence, computation, and characterization of nonsymmetric locally Lipschitz continuous (and, therefore, Clarke-differentiable) Markovian equilibrium for a class of infinite horizon multiagent competitive equilibrium models with capital, aggregate risk, public policy, externalities, one sector production, and incomplete markets. The class of models we consider is large, and examples have been studied extensively in the applied literature in public economics, macroeconomics, and financial economics. We provide sufficient conditions that distinguish between economies with isotone Lipschitizian Markov equilibrium decision processes (MEDPs) and those that have only locally Lipschitzian (but not necessarily isotone) MEDPs. As our fixed point operators are based upon order continuous and compact non-linear operators, we are able to provide sufficient conditions under which isotone iterative fixed point constructions converge to extremal MEDPs via successive approximation. We develop a first application of a new method for computing MEDPs in a system of Euler inequalities using isotone fixed point theory even when MEDPs are not necessarily isotone. The method is a special case of a more general mixed monotone recursive approach. We show MEDPs are unique only under very restrictive conditions. Finally, we prove monotone comparison theorems in Veinott's strong set order on the space of public policy parameters and distorted production functions.