Many important economic questions are best posed in a dynamic framework, where economic agents interact over time and where the past influences the environment. Examples include research and development races and resource extraction. Such dynamic strategic interaction among agents could be studied as stochastic games, where the evolution of "state variables" captures how the past influences the present at every instant. Stochastic games in which the evolution of state variables can be captured by differential equations are called differential games.
Solving such games requires reliance on dynamic programming techniques. The technical difficulties involved have meant that game theory texts in general have given the topic a wide berth. Academic research using such games has been mostly confined to a few specialised journals. This book brings together the various strands of knowledge on non-cooperative differential games for the first time. A great merit of the text is that it is, technique-wise, self-contained. The large number of worked examples enhances considerably the clarity of the material.
A somewhat puzzling aspect of the book is the importance it accords to the idea of "time consistency". Either dynamic strategy requires commitment (open loop) or equilibrium strategies are mutual-best responses (Nash equilibrium and its refinements). The notion of time consistency does not contribute meaningfully to this scheme. As defined, it has no game-theoretic foundation and merely adds confusion.
This apart, the authors must be commended on making technically difficult material accessible. Strategic interaction in continuous time gives rise to tech-nical problems that are clearly presented. The second part also serves as an excellent justification for the subject itself. This part develops applications that showcase the power of this class of game in analysing dynamic strategic interaction.
The book fills a large gap and will facilitate inclusion of differential games as part of mainstream game theory courses at advanced undergraduate and graduate levels. Teaching purposes aside, game theorists as well as PhD students will benefit a lot from this excellent new text. The book will enable researchers to add differential games to their arsenal of techniques in looking for the best modelling approach to address economic questions.
Arupratan Daripa is lecturer in economics and finance, Birkbeck College, University of London.
Differential Games in Economics and Management Science. First Edition
Author - Engelbert Dockner, Steffen Jorgensen, Ngo Van Long and Gerhard Sorger
ISBN - 0 521 63125 4 and 63732 5
Publisher - Cambridge University Press
Price - £55.00 and £19.95
Pages - 382