Dynamic Shapley Value and Dynamic Nash Bargaining

David Wing-kay Yeung
SRS Consortium, Hong Kong Shue Yan University, Hong Kong, China &
Center of Game Theory, St Petersburg State University, St Petersburg, Russia

Leon A. Petrosyan
Faculty of Applied Mathematics, St Petersburg State University, St Petersburg, Russia

Series: Mathematics Research Developments
BISAC: MAT011000




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This book is an important and innovative addition to textbooks in game theory. It provides a detailed discourse on the extension of two of the world’s most prominent cooperative game solutions – the seminal Shapley value in games with transferrable payoffs and the classic Nash bargaining scheme in games with non-transferrable payoffs – to a dynamic framework. The extension of these two classic cooperative solution concepts into a dynamic setting is not just of theoretical interest, but also allows many real-life cooperation situations – like global environmental management, nuclear disarmament, disease control, trade disputes and political unions – to be analyzed in an effective way.

This book provides: (i) A compendium of dynamic optimization techniques used in its analysis; (ii) a detailed disquisition on cooperative dynamic consistency; (iii) the extension of the Shapley Value to a dynamic framework; (iv) the establishment of a dynamic Nash bargaining paradigm; and (v) the incorporation of stochastic elements into the analyses. Interesting solvable examples are provided to illustrate the practicality and applicability of the dynamic Shapley value and dynamic Nash bargaining scheme in dynamic cooperation.


Foreword by Vladimir Mazalov

Chapter 1. Introduction

Chapter 2. Dynamic Optimization Techniques

Chapter 3. Cooperative Subgame Consistency

Chapter 4. Dynamic Shapley Value Imputation

Chapter 5. Dynamic Nash Bargaining

Chapter 6. Stochastic Extension



The book is written for researchers, graduate students and policy-makers interested in game theory, dynamic cooperation, microeconomics, and bargaining theory. The academic level of the materials is at post-graduate level, M.Sc, MPhil, PhD; research study, research references.
Professional people, groups or institutions: Universities, policy-making units, venture capitalists, business developers, governments and United Nations organizations would find it useful.
Nonprofessional people of industries: Historians interested in game theory or mathematics, and Bio writer interested in the life and contributions of Nobel laureates and legendary game theorists John Nash and Lloyd Shapley.

Professor Vladimir Turetsky, Ort Braude College of Engineering, Karmiel, Israel. To read the review, click here.

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