1st Edition

Reflexion and Control Mathematical Models

    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.



    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


    Novikov, Dmitry A.; Chkhartishvili, Alexander G.