Differential Games in Economics and Management Science
This book is a comprehensive, self-contained survey of the theory and applications of differential games. No prior knowledge of game theory is assumed, although a basic knowledge of linear algebra, ordinary differential equations and mathematical programming is required. This book is designed as a research resource for researchers and scholars as well as a text for advanced undergraduates and first year graduate students. Those in all aspects of economics, as well as in industrial organizations, decision sciences, management science, marketing, operations research and quantitative methods will benefit from this book.
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actions adjoint equation advertising assume assumption best reply brium capital stock chapter choose concave consider constant constraints control variables cost costate equations costate variables defined denote depend derive differential equation differential game Dockner dynamic game equilibrium strategies example feasible control path finite firm follower's follows game theory given Hamiltonian HJB equation holds implies infinite horizon leader linear quadratic Lipschitz continuous Markov perfect Nash Markovian Nash equilibrium Markovian strategies mode Nash equili noncooperative nondegenerate nondegenerate Markovian objective functional obtain open-loop Nash equilibrium open-loop strategies optimal control path optimal control problem optimal solution optimal value function output Pareto optimal payoff perfect Nash equilibrium profit quadratic differential resource right-hand side satisfied stationary Markovian Nash steady strategic form strategy profile subgame perfect switching symmetric system dynamics target path tion trajectory transversality condition trigger strategies utility function vector Wiener process yields zero