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This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact

Science: general issues --- Intertemporal choice --- anomaly --- behavioral economics --- time preference --- time-consistency --- Intertemporal choice --- anomaly --- behavioral economics --- time preference --- time-consistency

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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.

Research & information: general --- Mathematics & science --- 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 --- 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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This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While originating in economics, this theory now has applications in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity.Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players, as the number of players tends to infinity. This book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit.This groundbreaking book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics.

Convergence. --- Mean field theory. --- Many-body problem --- Statistical mechanics --- Functions --- A priori estimate. --- Approximation. --- Bellman equation. --- Boltzmann equation. --- Boundary value problem. --- C0. --- Chain rule. --- Compact space. --- Computation. --- Conditional probability distribution. --- Continuous function. --- Convergence problem. --- Convex set. --- Cooperative game. --- Corollary. --- Decision-making. --- Derivative. --- Deterministic system. --- Differentiable function. --- Directional derivative. --- Discrete time and continuous time. --- Discretization. --- Dynamic programming. --- Emergence. --- Empirical distribution function. --- Equation. --- Estimation. --- Euclidean space. --- Folk theorem (game theory). --- Folk theorem. --- Heat equation. --- Hermitian adjoint. --- Implementation. --- Initial condition. --- Integer. --- Large numbers. --- Linearization. --- Lipschitz continuity. --- Lp space. --- Macroeconomic model. --- Markov process. --- Martingale (probability theory). --- Master equation. --- Mathematical optimization. --- Maximum principle. --- Method of characteristics. --- Metric space. --- Monograph. --- Monotonic function. --- Nash equilibrium. --- Neumann boundary condition. --- Nonlinear system. --- Notation. --- Numerical analysis. --- Optimal control. --- Parameter. --- Partial differential equation. --- Periodic boundary conditions. --- Porous medium. --- Probability measure. --- Probability theory. --- Probability. --- Random function. --- Random variable. --- Randomization. --- Rate of convergence. --- Regime. --- Scientific notation. --- Semigroup. --- Simultaneous equations. --- Small number. --- Smoothness. --- Space form. --- State space. --- State variable. --- Stochastic calculus. --- Stochastic control. --- Stochastic process. --- Stochastic. --- Subset. --- Suggestion. --- Symmetric function. --- Technology. --- Theorem. --- Theory. --- Time consistency. --- Time derivative. --- Uniqueness. --- Variable (mathematics). --- Vector space. --- Viscosity solution. --- Wasserstein metric. --- Weak solution. --- Wiener process. --- Without loss of generality.