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

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.



Table of Contents


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 Dynamic Shapley Value and Dynamic Nash Bargaining of Professor Yeung and Professor Petrosyan provides a new evidence of their indisputable scientific authority in the field of Dynamic Games theory and applications.” READ MORE… – Professor Vladimir Turetsky, Ort Braude College of Engineering, Karmiel, Israel

“This book makes a significant contribution to the game theory applications and methodologies as it provides in depth theoretical and mathematical expansions of the seminal work of Shapley value and Nash bargaining to a dynamic framework. Though its analyses involve an advanced level of mathematics, the book is an excellent reference text for academics and economists interested in real-life cooperative studies like trade pact, environmental collaborations and joint technology development. The book also provides the fundamentals for dynamic cooperative analysis, and itself can be regarded as a front-running textbook on the dynamic cooperative game theory applications and methodologies, especially with the solution concept and technique of cooperative subgame consistency (that were originated by the authors). Also, the Nash-Petrosyan-Yeung dynamic bargaining solution and the Petrosyan-Yeung dynamic Shapley value imputation are sophisticated game theory solutions that serious economists in need to know in their research on real-life economic cooperation problems.” – Professor Sardar M. N. Islam (Naz) Ph. D., CPA, LL.B., M.A., Professor, VU Research; Professor of Business, Economics and Finance (2007 to 2017); Victoria University, Melbourne, Australia

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.

Additional information