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This book collects papers from the Special Issue "Singularly Perturbed Problems: Asymptotic Analysis and Approximate Solution", published in Axioms. These papers cover different aspects of singular perturbation theory and its applications: axiomatic approach in the analytic theory of singular perturbations; asymptotic solution of various types of singularly perturbed integral–differential and integral equations with weakly and rapidly varying kernels of the integral operators; propagation of two-dimensional periodic perturbations in a viscous continuously stratified fluid; asymptotic analysis of the stochastic linear–quadratic optimal control problem with two fast timescales in the dynamics; asymptotic solution of singularly perturbed Cauchy problem for different types of differential equations with "simple" turning points; asymptotic analysis of the complete Euclidean space controllability for different types of singularly perturbed differential systems with time delays; asymptotic solution of singularly perturbed systems in the critical case by the orthogonal projector method; application of the direct scheme method to asymptotic solution of one class of optimal control problems with three-tempo state variables; asymptotic analysis and solution of a cheap control linear quadratic zero-sum differential game; analysis of asymptotic behavior of the solutions for one class of singularly perturbed Neumann boundary value problems .

Research & information: general --- Mathematics & science --- Singularly Perturbed Differential Equations --- Singularly Perturbed Control Problems --- Singularly Perturbed Dynamic Games --- Asymptotic Analysis --- Asymptotic Solution

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We study the optimal design of a disinflation plan by a planner who lacks commitment. Having announced a plan, the Central banker faces a tradeoff between surprise inflation and building reputation, defined as the private sector's belief that the Central bank is committed to the plan. Some plans are harder to sustain: the planner recognizes that paving out future grounds with temptation leads the way for a negative drift of reputation in equilibrium. Plans that successfully create low inflationary expectations balance promises of lower inflation with dynamic incentives that make them more credible. When announcing the disinflation plan, the planner takes into account these anticipated interactions. We find that, even in the zero reputation limit, a gradual disinflation is preferred despite the absence of inflation inertia in the private economy.

United States --- Inflation --- Money and Monetary Policy --- Taxation --- Monetary Policy --- Stochastic and Dynamic Games --- Evolutionary Games --- Repeated Games --- Price Level --- Deflation --- Taxation, Subsidies, and Revenue: General --- Macroeconomics --- Monetary economics --- Public finance & taxation --- Inflation targeting --- Tax incentives --- Disinflation --- Prices --- Monetary policy

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This book focuses on various aspects of dynamic game theory, presenting state-of-the-art research and serving as a testament to the vitality and growth of the field of dynamic games and their applications. The selected contributions, written by experts in their respective disciplines, are outgrowths of presentations originally given at the 13th International Symposium of Dynamic Games and Applications held in Wrocław. The book covers a variety of topics, ranging from theoretical developments in game theory and algorithmic methods to applications, examples, and analysis in fields as varied as environmental management, finance and economics, engineering, guidance and control, and social interaction. The book is thematically organized into five parts: * Theoretical developments in differential and dynamic games; * Pursuit-evasion and guidance games; * Evolutionary games; * Stability and time consistency in cooperative games; * Applications and numerical approaches in environmental and renewable resource management, finance, insurance and economics, supply chains, and telecommunications. Featured throughout are useful tools and valuable resources for researchers, practitioners, and graduate students interested in dynamic games and their applications in applied mathematics, engineering, economics, and management science. Also included in the volume is a special tribute to Arik Melikyan, honoring his memory and the many contributions he made to the field of dynamic games.

Dynamic games. --- Game theory -- Congresses. --- Game theory. --- Differential games --- Stochastic processes --- Business & Economics --- Mathematics --- Economic Theory --- Algebra --- Physical Sciences & Mathematics --- Differential games. --- Stochastic processes. --- Random processes --- Games, Differential --- Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Biomathematics. --- Game Theory, Economics, Social and Behav. Sciences. --- Game Theory. --- Applications of Mathematics. --- Appl.Mathematics/Computational Methods of Engineering. --- Genetics and Population Dynamics. --- Probabilities --- Game theory --- Genetics --- Mathematical and Computational Engineering. --- Biology --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Heredity --- Mutation (Biology) --- Variation (Biology) --- Engineering --- Engineering analysis --- Mathematical analysis --- Games, Theory of --- Theory of games --- Mathematical models --- Math --- Science

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Central bank digital currencies (CBDCs) promise many benefits but, if not well designed, they could have undesired consequences, including for monetary policy. Issuing an unremunerated CBDC or a wholesale CBDC does not change the objectives of monetary policy or the operational framework for monetary policy. CBDCs can, however, induce changes in the retail, wholesale and cross border payments that have negative spillover effects on monetary policy, through their effects on money velocity, bank deposit disintermediation, volatility of bank reserves, currency substitution, and capital flows. Countries most vulnerable are those with banking systems dominated by small retail deposits and demand deposits, low levels of digital payments and weak macro fundamentals. Proposed CBDC design features, such as caps on CBDC holdings and unremunerating the CBDC can moderate disintermediation risks, but they are not sufficient. Central banks will need to ensure that unintended macroeconomic risks are comprehensively identified and mitigated.

United States --- Macroeconomics --- Economics: General --- Industries: Financial Services --- Money and Monetary Policy --- Banks and Banking --- Islamic Banking and Finance --- Noncooperative Games --- Stochastic and Dynamic Games --- Evolutionary Games --- Repeated Games --- Market Structure and Pricing: General --- Demand for Money --- Monetary Systems --- Standards --- Regimes --- Government and the Monetary System --- Payment Systems --- Monetary Policy --- Central Banks and Their Policies --- Management of Technological Innovation and R&D --- Technological Change: Choices and Consequences --- Diffusion Processes --- Banks --- Depository Institutions --- Micro Finance Institutions --- Mortgages --- Information and Internet Services --- Computer Software --- Other Economic Systems: Public Economics --- Financial Economics --- Monetary Policy, Central Banking, and the Supply of Money and Credit: General --- Economic & financial crises & disasters --- Economics of specific sectors --- Banking --- Distributed ledgers --- Monetary economics --- Technology --- Financial institutions --- Money --- Financial services --- Central Bank digital currencies --- Commercial banks --- Velocity of money --- Islamic banking --- Monetary base --- Currency crises --- Informal sector --- Economics --- Financial services industry --- Technological innovations --- Banks and banking --- Islamic countries --- Money supply

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Financial inclusion is a key policy objective that central banks, especially those in emerging and low-income countries, are considering for retail central bank digital currency (CBDC). If properly designed to address the barriers to financial inclusion, CBDCs have the opportunity to gain acceptance by the financially excluded for digital payments. CBDC can then serve as an entry point to the broader formal financial system. CBDC has special aspects that may benefit financial inclusion, such as being a risk-free and widely acceptable form of digital money, availability for offline payments, and potentially lower costs and greater accessibility. However, CBDC is not a panacea to financial inclusion, and additional experience is needed to fully understand its potential impact.

Banking --- Banks and banking, Central --- Banks --- Central Bank digital currencies --- Central Banks and Their Policies --- Clearinghouses --- Computer Software --- Demand for Money --- Depository Institutions --- Diffusion Processes --- Digital financial services --- Distributed ledgers --- Economic & financial crises & disasters --- Economic sectors --- Economics of specific sectors --- Economics: General --- Evolutionary Games --- Finance --- Finance: General --- Financial inclusion --- Financial Institutions and Services: Government Policy and Regulation --- Financial Markets and the Macroeconomy --- Financial markets --- Financial services industry --- Financial services --- Government and the Monetary System --- Industries: Financial Services --- Information and Internet Services --- Macroeconomics --- Management of Technological Innovation and R&D --- Market Structure and Pricing: General --- Micro Finance Institutions --- Monetary Policy --- Monetary policy --- Monetary Systems --- Mortgages --- Noncooperative Games --- Payment Systems --- Payment systems --- Regimes --- Repeated Games --- Standards --- Stochastic and Dynamic Games --- Technological Change: Choices and Consequences --- Technological innovations --- Technology