In this book I develop a theory of complexity for economics and manage­ ment sciences. This book is addressed to the mathematically or analytically oriented economist, psychologist or management scientist. It could also be of interest to engineers, computer scientists, biologists, physicists and ecologists who have a constant desire to go beyond the bounds of their respective disciplines. The unifying theme is: we live in a complex world, but how can we cope with complexity? If the book has made the reader curious, and if he looks at modelling, problem recognition and problem solving within his field of competence in a more "complex" way, it will have achieved its goal. The starting point is the recognition that complexity is a well-defined concept in mathematics (e.g. in topological dynamics), computer science, information theory and artificial intelligence. But it is a rather diffuse concept in other fields, sometimes it has only descriptive value or even worse, it is only used in a colloquial sense. The systematic investigation of complexity phenomena has reached a mature status within computer science. Indices of computer size, capacity and performance root ultimately in John von Neumann's paradigmatic model of a machine, though other 1 roots point to McCulloch and Pitts, not to forget Alan Turing. Offsprings of this development include: -complexity of formal systems and recursiveness; -cellular automata and the theory of self-reproducing machines; -theory of program or computational complexity; -theory of sequential machines; -problem solving, cognitive science, pattern recognition and decision processes.

Inhalt

1 Introduction to Complex Systems.- 1.1 Finite Complex Systems.- 1.2 Some Concepts of Complexity.- 1.3 Fundamental Issues of Complexity.- 1.4 Multi-level System and Control.- 1.5 Design and Algebraic Systems.- 1.6 Models Using Catastrophe Theory.- 1.7 Aspects of FCS Modelling.- 1.8 Computer Models and Man Machine Interaction.- Note.- References.- 2* Mathematics of Machines, Semigroups and Complexity.- 2.1 Finite State Machines.- 2.2 Definitions and Bounds of Complexity.- 2.3 Machines and Semigroups.- 2.4 The Krohn-Rhodes Prime Decomposition Theorem for Finite Semigroups and Machines.- 2.5 An Application of the Prime Decomposition Theorem - Some Results on Combinatorial Semigroups.- 2.6 Calculating the Complexity of a Transformation Semigroup.- 2.7 The Generalized Model.- References.- 3 Complexity and Dynamics.- 3.1 Introduction and Motivation.- 3.2 Competitive Processes and Dynamical Systems.- 3.3 Description of a Dynamic System.- 3.4 Axioms of Complexity.- 3.5 Evolution Complexity.- 3.6 Dynamic Systems of Resource Depletion.- 3.7 Complexity in Thom's Program.- 3.8 Policy Conclusions.- Notes.- References.- 4 Structural Characteristics in Economic Models.- 4.1 Introduction.- 4.2 Preliminary Considerations.- 4.3 Decomposable Systems.- 4.4 Systems Modelling and Complexity.- 4.5 Structure of the Model.- 4.6 The Model's Basic Set of Relationships.- 4.7 Evaluation of Complexity.- 4.8 Discussion.- 4.9 Comparison with some Studies on the Economics of Organization.- Note.- References.- 5 Complexity, Bounded Rationality and Problem-Solving.- 5.1 Introduction.- 5.2 Bounded Rationality.- 5.3 Problem Solving.- 5.4 An Overview of Algorithmic Complexity and Problem-Solving.- 5.5 A Case in Heuristics: General Problem-Solving (GPS).- 5.6 Planning.- 5.7 Conclusions.- Appendix: Problem-Solving for Energy Technology Assessment.- Notes.- References.- 6 Complexity and Decision Rules.- 6.1 Introduction.- 6.2 Background and Motivation.- 6.3 Choice Processes and Complexity.- 6.4 An Example of a Decision or Search Rule.- 6.5 A Social Choice Machine.- 6.6 Complexity of Decision Rules.- 6.7 A Construction of Compatible Decision Rules.- 6.8 Summary and Extension.- Notes.- References.- 7 Complexity and Organizational Decision-Making.- 7.1 Introduction.- 7.2 Organizational Structures and Performance.- 7.3 Organizations and Environments.- 7.4 A Real-time Organization.- 7.5 Information Technology.- 7.6 Costs of Information Processing.- 7.7 A Simple Machine Model of Organizational Design.- 7.8 Organizational Malfunctioning and Design.- 7.9 The Case of Line Organization.- 7.10 The Parallel Processing Line.- 7.11 The Case of Staff Organization.- 7.12 The Staff Acting as an Input Filter.- 7.13 Optimization Problem of the Staff Design.- 7.14 The Alternately Processing Staff.- 7.15 The Parallel Processing Staff.- 7.16 Some Practical Aspects of Organizational Design.- Notes.- References.- Index of Names.- Index of Subjects.