Jerzy Filar - Böcker

This book is devoted to a unified treatment of Competitive Markov Decision Processes. It examines these processes from the standpoints of modeling and of optimization, providing newcomers to the field with an accessible account of algorithms, theory, and applications, while also supplying specialists with a comprehensive survey of recent developments. The treatment is self-contained, requiring only some knowledge of linear algebra and real analysis. Topics covered include: Mathematical programming: Markov decision processes (the non-competitive case), and stochastic games via mathematical programming.- Existence, structure and applications: Summable stochastic games, average-reward stochastic games and applications and special classes of stochastic games.- Appendices on: matrix games, bimatrix games and nonlinear programming; a theorem of Hardy and Littlewood; Markov chains; and complex varieties and the limit discount equation.

This work focuses on the application of dynamic game theory and control theory to analyze a number of important issues in the interaction between economic and environmental problems. The authors provide research results, mathematical models and prescriptions for public policy tools to prevent economic and natural systems from taking unsustainable development paths. The book should be of interest to research workers in industry and university, including engineers, mathematicians, economists and public policy-makers.

Modem game theory has evolved enonnously since its inception in the 1920s in the works ofBorel and von Neumann and since publication in the 1940s of the seminal treatise "Theory of Games and Economic Behavior" by von Neumann and Morgenstern. The branch of game theory known as dynamic games is-to a significant extent-descended from the pioneering work on differential games done by Isaacs in the 1950s and 1960s. Since those early decades game theory has branched out in many directions, spanning such diverse disciplines as math- ematics, economics, electrical and electronics engineering, operations research, computer science, theoretical ecology, environmental science, and even political science. The papers in this volume reflect both the maturity and the vitalityofmodem day game theoryin general, andofdynamic games, inparticular. The maturitycan be seen from the sophistication ofthe theorems, proofs, methods, and numerical algorithms contained in these articles.The vitality is manifested by the range of new ideas, new applications, the numberofyoung researchers among the authors, and the expanding worldwide coverage of research centers and institutes where the contributions originated.

This book collects some recent works on the application of dynamic game and control theory to the analysis of environmental problems. This collec­ tion of papers is not the outcome of a conference or of a workshop. It is rather the result of a careful screening from among a number of contribu­ tions that we have solicited across the world. In particular, we have been able to attract the work of some of the most prominent scholars in the field of dynamic analyses of the environment. Engineers, mathematicians and economists provide their views and analytical tools to better interpret the interactions between economic and environmental phenomena, thus achiev­ ing, through this interdisciplinary effort, new and interesting results. The goal of the book is more normative than descriptive. All papers include careful modelling of the dynamics of the main variables involved in the game between nature and economic agents and among economic agents themselves, as well-described in Vrieze's introductory chapter. Fur­ thermore, all papers use this careful modelling framework to provide policy prescriptions to the public agencies authorized to regulate emission dy­ namics. Several diverse problems are addressed: from global issues, such as the greenhouse effect or deforestation, to international ones, such as the management of fisheries, to local ones, for example, the control of effluent discharges. Moreover, pollution problems are not the only concern of this book.