An interval condensing method for the uniform approximation of extremal fixed points of isotone operators with applications to Markov equilibrium for stochastic OLG models with nonclassical production

An order based approach is developed to provide sufficient conditions for the existence, characterization and computation of Markovian equilibrium decision processes (MEDP) and stationary Markov equilibrium (MEDP). The production technologies allowed here, although reduced form, permit equilibrium distortions such as public policy distortions, social security, monetary equilibrium, and production nonconvexities. An important contribution is the constructive nature of the existence theorems and proofs, which in turn, implies a direct route for computational and approximation methods. In particular, existence of equilibrium is generated on a functional space by an iterative monotone operator, which by its nature is not subject to problems of nonexistence and indeterminacies in related work. Additionally, for the same class of economies, a interval condensing method is presented for generating construction, characterization and numerical approximation of MEDP, which greatly simplifies applicability and reduces restrictions for computation. An adaptation of the monotone map method is created by constructing the MEDP as the fixed point of a monotone sequence of uniformly convergent condensing intervals. In addition, it is proven that the numerical approximation implementation which follows the interval method converges uniformly to the theoretical MEDP and error bounds are given by the convergence of the operator. Finally, examples and possible extensions conclude.