Reflexion and control: mathematical models (Q2873814)

The aim of this book is to present modern approaches to mathematical modeling of reflexive processes in control. The authors consider reflexive games, that describe the game theoretical interaction of agents making decisions based on a hierarchy of beliefs regarding essential parameters (informational reflexion), decision principles used by opponents (strategic reflexion), 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., and uniform description of many psychological, sociological phenomena connected with reflexion, implicit control, informational control via the mass media, reflexion in chess, art works, etc.NEWLINENEWLINEThe book is structured in four chapters. Chapter 1 presents the model of individual decision-making, some major solution concepts of noncooperative games. Necessary assumptions imposed on awareness and mutual awareness of agents are discussed according to these solution concepts. Chapter 2 defines an informational equilibrium and analyses its properties. First, informational reflexion in two player games is described. Then, the general model is provided, i.e. a characterization of the awareness structure adopted by reflexive game participants in their decision making is given. Also, the notion of awareness structure complexity is introduced. Next, graph of a reflexive game is described as an analysis tool for the properties of an informational equilibrium. Further, the attention is focused on studying the influence of reflexion ranks on agents' gains, as well as on scrutinizing the relationship between an awareness structure and an informational equilibrium. The last part of the chapter deals with stability of an informational equilibrium, modeling of informational actions, as well as formulating informational control problems and examine their properties. The Chapter 3 studies models of strategic reflexion. First, the problem of maximal rational rank of strategic reflexion in bimatrix games is solved. Further, the finiteness of reflexion rank, which follows from limited data processing capabilities of humans is investigated. Finally, the reflexive partitions method for reflexive control problems is described. In Chapter 4 a series of applied models of reflexive games (implicit control, informational control by mass media, as well as reflexion in psychology and art works) are considered. Numerous references provide detailed information on the capabilities of this approach in various applied problems. An important part of the chapter is dedicated to applied models of informational and reflexive control in economic systems, military problems and other fields.NEWLINENEWLINESeveral approaches to reading this book can be proposed. The first one is linear (successive reading of all chapters). The second approach is intended for a reader mostly interested in formal models (observational reading of Chapters 2-3 and glancing over the examples in Chapter 4). The third approach aims at a reader concerned with practical interpretations rather than mathematical subtleties (observational reading of the Introduction, the examples in Chapter 4 and the Conclusion).NEWLINENEWLINEThe present book is intended for experts in decision making and control of systems of an interdisciplinary nature, as well as for undergraduate and postgraduate students.