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In this study we offer a new approach to proving the differentiability of the value function, which complements and extends the literature on dynamic programming. This result is then applied to the analysis of equilibrium in the recent class of monetary economies developed in [Lagos, R., Wright, R., 2005. A unified framework for monetary theory and policy analysis. journal of Political Economy 113, 463-484]. For this type of environments we demonstrate that the value function is differentiable and this guarantees that the marginal value of money balances is well defined.

Price Dynamics, Social Choice, Voting Methods, Probability and Chaos -- Pareto Optima and Equilibria: The Finite Dimensional Case -- The Optimality of Regulated Pricing: A General Equilibrium Analysis -- Value Allocations: An Exposition -- On Extensions of the Cournot-Nash Theorem -- Thick and Thin Market Nonatomic Exchange Economies -- Examples of Excess Demand Functions on Infinite-Dimensional Commodity Spaces -- On Perfectly Competitive Economies: Loeb Economies -- Nonstandard Analysis and Infinite Economies: The Cournot-Nash Solution -- Remarks Related to Finitely Additive Exchange Economies -- Value and Fairness.

This book is concerned with the analysis, optimization and controllability of time-discrete dynamical systems and games under the aspect of stability, controllability and (for games) cooperative and non-cooperative treatment. The investigation of stability is based on Lyapunov's method which is generalized to non-autonomous systems. Optimization and controllability of dynamical systems is treated, among others, with the aid of mapping theorems such as implicit function theorem and inverse mapping theorem. Dynamical games are treated as cooperative and non-cooperative games and are used in order to deal with the problem of carbon dioxide reduction under economic aspects. The theoretical results are demonstrated by various applications