Reflexion and Control: Mathematical Models, 1st Edition (Hardback) book cover

Reflexion and Control

Mathematical Models, 1st Edition

By Dmitry A. Novikov, Alexander G. Chkhartishvili

CRC Press

298 pages

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Hardback: 9781138024731
pub: 2014-03-03
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pub: 2014-03-03
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This book is dedicated to modern approaches to mathematical modeling of reflexive processes in control. The authors consider reflexive games that describe the gametheoretical interaction of agents making decisions based on a hierarchy of beliefs regarding (1) essential parameters (informational reflexion), (2) decision principles used by opponents (strategic reflexion), (3) beliefs about beliefs, and so on. Informational and reflexive equilibria in reflexive games generalize a series of well-known equilibrium concepts in noncooperative games and models of collective behavior. These models allow posing and solving the problems of informational and reflexive control in organizational, economic, social and other systems, in military applications, etc. (the interested reader will find in the book over 30 examples of possible applications in these fields) and describing uniformly many psychological/sociological phenomena connected with reflexion, viz., implicit control, informational control via the mass media, reflexion in chess, art works, etc. The present book is intended for experts in decision making and control of systems of an interdisciplinary nature, as well as for undergraduates and postgraduates.

Table of Contents


1 Reflexion in decision-making

1.1 Individual decision-making

1.2 Interactive decision-making: Games and equilibria

1.3 General approaches to the description of informational and strategic reflexion

2 Informational reflexion and control

2.1 Informational reflexion in two-player games

2.2 Awareness structure of games

2.3 Informational equilibrium

2.4 Graph of a reflexive game

2.5 Regular awareness structures

2.6 Reflexion rank and informational equilibrium

2.7 Stable informational equilibria

2.8 True and false equilibria

2.9 The case of observable actions of agents

2.10 Reflexive games and Bayesian games

2.11 Informational control

2.12 Modeling of informational impact

2.13 Set-type awareness structures

2.14 Transformation of awareness structure

2.15 Concordant informational control

2.16 Reflexion in planning mechanisms

3 Strategic reflexion and control

3.1 Strategic reflexion in two-player games

3.2 Reflexion in bimatrix games and games of ranks

3.3 Boundedness of reflexion ranks

3.4 Reflexive structures and reflexive control

4 Applied models of informational and reflexive control

4.1 Implicit control

4.2 The mass media and informational control

4.3 Reflexion in psychology

4.3.1 Playing chess

4.3.2 Transactional analysis

4.3.3 The Johari window

4.3.4 Ethical choice

4.4 Reflexion in bélles-léttres

4.5 Reflexive search games

4.6 Manufacturers and intermediate sellers

4.7 The scarcity principle

4.8 Joint production

4.9 Market competition

4.10 Lump sum payments

4.11 Sellers and buyers

4.12 Customers and executors

4.13 Corruption

4.14 Bipolar choice

4.15 Active expertise: Informational reflexion

4.16 The cournot oligopoly: Informational reflexion

4.17 Resource allocation

4.18 Insurance

4.19 Product advertizing

4.20 The hustings

4.21 Rank-order tournaments

4.22 Explicit and implicit coalitions in reflexive games

4.23 Active forecast

4.24 Social networks

4.25 Mob control

4.26 The reflexive partitions method

4.26.1 Diffuse bomb

4.26.2 The colonel Blotto game

4.26.3 The Cournot oligopoly: strategic reflexion

4.26.4 The consensus problem

4.26.5 Active expertise: strategic reflexion

4.26.6 Transport flows and evacuation

4.26.7 A stock exchange



Subject index

About the Authors

Novikov\, Dmitry A.; Chkhartishvili\, Alexander G.

About the Series

Communications in Cybernetics, Systems Science and Engineering

Communications in Cybernetics, Systems Science and Engineering is a cross-disciplinary book series devoted to theoretical and applied research contributions to cybernetics, systems science and engineering. The series aims to publish the highest quality monographs and edited volumes on the most recent advances and innovative applications in the relevant areas of investigation, catering to a rapidly growing worldwide interest in a cybernetic and systemic methodology with an ever-increasing capacity to deal with new challenges in a way that traditional science cannot. The CCSSE series aims to become a comprehensive theoretical, practical, international, multi- and interdisciplinary database of, reference work on and guide to issues in these fields of research and the strategies required for better implementation in the context of environmental protection and sustainable social and economic development. Communications in Cybernetics, Systems Science and Engineering aims at all working in the theoretical and applied fields of cybernetics, systems science and engineering, e.g. academics, researchers and consultants in cybernetics and systems, computer and information scientists, development and systems engineers, mathematicians, librarians, management cyberneticists and systemists, medical scientists, educators, and intelligent and manufacturing engineers in industry. It will also be of interest to leading decision- and policy-makers.

Michael C. Jackson, University of Hull, UK
Jerzy Jozefczyk, Wroclaw University of Technology, Poland
Doncho Petkov, Eastern Connecticut State University, USA
Vladimir Tsurkov, Russian Academy of Sciences, Russia
Shouyang Wang, Chinese Academy of Sciences, P.R. China

The principal areas covered by the Communications in Systems Science and Engineering series include, but are not limited to:
1) All fields of systems research, cybernetics and the interdisciplinary study of cybernetics and systems in the widest sense, such as: Artificial intelligence • Automation and robotics • Biocybernetics • Complex and fuzzy systems • Computer simulation • Cross-disciplinary problem-solving • Cybernetics/systems analysis modeling and simulation • Ecosystems • Information theories • Interrelations  between cybernetics/systems and other sciences • Management cybernetics and systems (including soft systems methodology, Ackoff’s interactive planning, Churchman’s theory of inquiring systems, and other approaches) • Natural language • Philosophy of cybernetics and systems • Theoretical and experimental knowledge of various categories of systems, such as adaptive, anticipatory, autopoietic, cellular, chaotic, dynamic, economic and social, hierarchical, immune-like, intelligent, knowledge-based, learning, neural, quantum, self-organizational, self-producing and self-referential;

2) All areas of systems engineering and the spectrum of engineering activity, decision-making, management of products and services, and processes of all types. Focused on comprehensive approaches to practical applications and developments of "hard" and "soft" systems and cybernetic methodologies, including, but not limited to: Cognitive ergonomics • Conceptual architecture • Configuration management during system development • Decision-making • Environmental policy • Human-machine interaction • Identification of user requirements and technological specifications • Integration of new systems with legacy systems • Integrated product and process development • Issue formulation analysis and modeling • Modeling of uncertainty, maintenance over an extended lifecycle and re-engineering of systems • Multicriteria decision-making • Numerical simulation and qualitative modeling of complex systems • Risk assessment and safety • Sustainable development • System identification, operational test and evaluation • Systems analysis, engineering processes and methods such as optimization, modeling and simulation • Trade-off of design concepts.

C.L. Philip Chen, University of Macau, P.R. China
Zengru Di, Beijing Normal University, P.R. China
Raul Espejo, Syncho Ltd. and World Organization of Systems and Cybernetics, UK
Keith W. Hipel, University of Waterloo, Canada
Baoding Liu, Tsinghua University, China
Nagendra Nagarur, State University of New York at Binghamton, USA
John Pourdehnad, University of Pennsylvania, USA
Brian Howard Rudall, Institute of the World Organisation of Systems and Cybernetics and Bangor University, UK
Rudolf Scheidl, Johannes Kepler University of Linz, Austria
Markus Schwaninger, Institute of Management, University of St. Gallen, Switzerland

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Subject Categories

BISAC Subject Codes/Headings:
TECHNOLOGY & ENGINEERING / Engineering (General)