Game Theory and Applications. Volume 16


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

Vladimir Mazalov (Editor)
Institute of Applied Mathematical Research, Karelia Research Center of Russian Academy of Sciences, Karelia, Russia

Series: Game Theory and Applications
BISAC: GAM000000

This book brings together papers of well-known specialists in game theory and adjacent problems. It presents the basic results in dynamic games, stochastic games, applications of game theoretical methods in ecology and economics and methodological aspects of game theory.

Special attention was given to problems in dynamic games under partial information and to the development of numerical methods for high-dimensional games (there is an increasing focus on this arena as recent theory is leading to solution methods for problems which were heretofore quite intractable). The interdisciplinary aspects touched upon were related to dynamical systems via replicator dynamics, with probability (measure-valued processes), statistical mechanics (kinetic equation, non-equilibrium behaviour) and max-plus (tropical or idempotent) mathematics.

In this volume, we publish the review of Martin Shubik (The Present and Future of Game Theory) and the contributions presenting extending versions of the talks given at the workshop “Game Theory for Finance, Social and Biological Sciences”, held in Warwick 14-17 of April 2010. The conference was exclusively marked by a rare natural event: the eruption of an Icelandic volcano Eyjafjallajökull, which blocked the functioning of most of the airlines, turning the return trip into an adventurous enterprise for many participants. (Imprint: Nova)

Table of Contents

Table of Contents


Chapter 1. A Robust Control Approach to Option Pricing: The Uniqueness Theorem
(Pierre Bernhard and Naima El-Farouq, INRIA Sophia Antipolis-mediterranee, France, and others)

Chapter 2. Existence and Uniqueness of Nash Equilibria in a Simple Lanchester Model of the Costs of Customer Churn
(Jane M. Binner, Leslie R. Fletcher and Vassili Kolokoltsov, Sheffield Management School, Faculty of Electrical Engineering, Sheffield, UK, and others)

Chapter 3. The Game-Theoretical Model of Service Selection in Company
(Vladimir M. Bure and Anna A. Sergeeva, Saint Petersburg State University, Saint Petersburg, Russia)

Chapter 4. Numerical Approximation of Nash Equilibria for a Class of Non-Cooperative Differential Games
(Simone Cacace, Emiliano Cristiani and Maurizio Falcone, Dipartimento di Matematica, Sapienza, Universita di Roma, Rome, Italy)

Chapter 5. Public Goods in Networks: A Statistical Mechanics Approach
(Luca Dall’Asta, Paolo Pin and Abolfazl Ramezanpour, Department of Applied Science and Technology, Politecnico di Torino, Turin, Italy, and others)

Chapter 6. Network Congestion, Braess Paradox and Urban Expressway System
(Baomin Dong, School of Economics, Zhejiang University, Hangzhou, China)

Chapter 7. Game-theoretical Model of Service Quality Choice:
Portuguese Mobile Service Market
(Margarita A. Gladkova, Nikolay A. Zenkevich and Anna A. Sorokina, Graduate School of Management, Saint Petersburg State University, Saint Petersburg, Russia)

Chapter 8. Paul Samuelson’s Critique and Equilibrium Concepts in Evolutionary Game Theory
(Reinoud Joosten, School of Management & Governance, University of Twente, Enschede, The Netherlands)

Chapter 9. Price Stackelberg Competition and Capacity Constrains
(Ling-peng Meng, Chuan-feng Han and Jian-min Wang, School of Economics & Management, Tongji University, Shanghai, China, and others)

Chapter 10. An Inter-group Conflict Model Integrating Perceptions of Threat and Vested Interest: Extending Rational Choice to Incorporate Psychological Dynamics
(Glenn Pierce, Christopher Boulay and Mikhail Malyutov, School of Criminology and Criminal Justice, Northeastern University, Boston, MA, USA, and others)

Chapter 11. Product Differentiation in the Presence of Social Interactions of Consumers
(Fernando Pigeard de Almeida Prado, Department of Computing and Mathematics, FFCLRP, University of Sao Paulo, Brazil)

Chapter 12. A Class of Differential Games with Random Terminal Time
(Ekaterina V. Shevkoplyas and Sergey Yu. Kostyunin, Saint Petersburg State University, Saint Petersburg, Russia)

Chapter 13. The Present and Future of Game Theory
(Martin Shubik, Yale University, New Haven, CT, USA)


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