Reflexion and Control : Mathematical Models

The book considers the basics of mathematical modeling of reflexive processes in control. The models of informational and strategic reflexion allow describing and studying the behavior of reflexing subjects, investigating the relationship between payoffs gained by agents and their reflexion ranks, posing and solving the problems of informational and reflexive control in organizational, economic, social and other systems, and military applications among others (the book contains over 30 examples of possible applications in these fields), describing uniformly many phenomena connected with reflexion, viz., implicit control, informational control via the mass media and reflexion in psychology.

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.