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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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International macroeconomic policy coordination is generally considered to be made less likely—and less profitable—by the presence of uncertainty about how the economy works. The present paper provides a counter-example, in which increased uncertainty about portfolio preference of investors makes coordination of monetary policy more beneficial. In particular, in the absence of coordination monetary authorities may respond to financial market uncertainty by not fully accommodating demands for increased liquidity, for fear of bringing about exchange rate depreciation. Coordinated monetary expansion would minimize this danger. A theoretical model incorporating an equity market is developed, and the stock market crash of October 1987 is discussed in the light of its implications for monetary policy coordination.

Finance: General --- Foreign Exchange --- Investments: Stocks --- Macroeconomics --- Stochastic and Dynamic Games --- Evolutionary Games --- Repeated Games --- Financial Markets and the Macroeconomy --- Monetary Policy --- Pension Funds --- Non-bank Financial Institutions --- Financial Instruments --- Institutional Investors --- General Financial Markets: General (includes Measurement and Data) --- Price Level --- Inflation --- Deflation --- Macroeconomics: Consumption --- Saving --- Wealth --- Investment & securities --- Finance --- Currency --- Foreign exchange --- Stocks --- Stock markets --- Asset prices --- Exchange rates --- Consumption --- Financial institutions --- Financial markets --- Prices --- National accounts --- Stock exchanges --- Economics --- United States

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The Special Issue “Game Theory” of the journal Mathematics provides a collection of papers that represent modern trends in mathematical game theory and its applications. The works address the problem of constructing and implementation of solution concepts based on classical optimality principles in different classes of games. In the case of non-cooperative behavior of players, the Nash equilibrium as a basic optimality principle is considered in both static and dynamic game settings. In the case of cooperative behavior of players, the situation is more complicated. As is seen from presented papers, the direct use of cooperative optimality principles in dynamic and differential games may bring time or subgame inconsistency of a solution which makes the cooperative schemes unsustainable. The notion of time or subgame consistency is crucial to the success of cooperation in a dynamic framework. In the works devoted to dynamic or differential games, this problem is analyzed and the special regularization procedures proposed to achieve time or subgame consistency of cooperative solutions. Among others, special attention in the presented book is paid to the construction of characteristic functions which determine the power of coalitions in games. The book contains many multi-disciplinary works applied to economic and environmental applications in a coherent manner.

pursuit --- control functions --- integral constraints --- strategies --- value of the game --- decision-making --- game theory --- project management --- differential games --- cooperative differential games --- Time Consistency --- IDP-core --- IDP dominance --- two-sided platform market --- pricing --- Hotelling’s duopoly on the plane --- Nash equilibrium --- optimal location of platforms --- prescribed duration --- characteristic function --- environmental resource management --- pollution control --- discrete-time games --- cooperation --- the core --- linear transformation --- time consistency --- multistage game --- chance moves --- subgame perfect equilibria --- cooperative trajectory --- imputation distribution procedure --- random time horizon --- time until failure --- discounted equilibrium --- weibull distribution --- chen distribution --- equivalence principle --- cooperative game --- satisfaction criteria --- proportional value --- axiomatization --- cooperative stochastic game --- strong subgame consistency --- core --- dynamic games --- multicriteria games --- Nash bargaining solution --- dynamic stability --- rational behavior conditions --- Shapley-Solidarity value --- coalition structure --- potential --- bidding mechanism

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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