Barriers and Bounds to Rationality

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ISBN: 9780691026763 | 0691026769
Cover: Hardcover
Copyright: 4/6/1998

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Peter Albin is known for his seminal work in applying the concepts of adaptive dynamical systems, first developed by biologists and physicists, to the study of economic systems. This book is a collection of his pathbreaking articles on the application of cellular automata and complexity theory to economic problems. Duncan Foley provides a thoughtful introduction in which he reviews the disparate analytical sources of Albin's work in the theories of nonlinear dynamical systems, economic dynamics, cellular automata, linguistic and computational complexity, and bounded rationality. Albin has analyzed economic systems as interactions of highly complex components (i.e., intelligent human beings). He uses the theories of generative linguistics and cellular automata to establish that the complexity level of economic systems is, in principle at least, that of a Turing machine or general-purpose computer, establishing that classic economic approaches to the problems of household and firm choice, macroeconomic prediction, and policy evaluation may give rise to undecidable propositions and uncomputable functions. He develops simple models of dynamic economic interaction based on cellular automata which illustrate the inherent complexity of economic interactions and the resulting challenge they pose to traditional theories of rational economic behavior. These models explore the dynamics of the business cycle, decentralized market trading, and the emergence of cooperation in a novel local-interaction version of the repeated prisoners' dilemma game. Albin's work provides a unique and important perspective on economic systems.

Preface

xiii

(20)

Acknowledgments

xxxiii

1 Introduction

(70)

1.1 Dynamical systems

(14)

1.1.1 Linear dynamical systems

(3)

1.1.2 Nonlinear dynamical systems

(8)

1.1.3 Cellular automata as models of nonlinear dynamical systems

(2)

1.2 Dynamical systems in social and physical science

(6)

1.2.1 Local and global interaction

(1)

1.2.2 Topology and geometry in physical and social models

(2)

1.2.3 Time and causality

(1)

1.2.4 Identity and diversity

(2)

1.3 Economic models of fully rational behavior

(17)

1.3.1 The rational choice program

(2)

1.3.2 Individual decision models-intertemporal optimization

(1)

1.3.3 The finite-horizon Ramsey problem

(3)

1.3.4 Market models

(5)

1.3.5 Game theory models

(7)

1.4 Definitions and measures of complexity

(8)

1.4.1 Computational complexity

(1)

1.4.2 Linguistic complexity

(2)

1.4.3 Machine complexity

(2)

1.4.4 Decidability, computational complexity, and rationality

(1)

1.4.5 Dynamical systems and computational complexity

(1)

1.5 Complexity in cellular automata

(5)

1.5.1 Complexity types

(2)

1.5.2 Computability, predictability, and complexity in cellular automata

(1)

1.6 Modeling complex social and economic interactions

(11)

1.6.1 Self-referencing individual agents

(2)

1.6.2 Organizations

(1)

1.6.3 Industries and economies

(2)

1.6.4 Markets

(3)

1.6.5 The local interaction multiperson Prisoners' Dilemma

(3)

1.7 Complexity, rationality, and social interaction

(4)

1.7.1 How complex are social systems?

(2)

1.7.2 How smart do agents need to be?

(1)

1.8 Toward a robust theory of action and society

(5)

2 The Metalogic of Economic Predictions, Calculations, and Propositions

(32)

2.1 Introduction

(3)

2.2 Preliminaries: Automata and structural formations

(7)

2.2.1 Finite automata

(1)

2.2.2 Finite formations

(2)

2.2.3 Generalized formations and finite surrogates

(1)

2.2.4 General computation and computability

(3)

2.3 Undecidability in generalized formations

(8)

2.3.1 An economy with finite automaton components

(1)

2.3.2 Structural properties of a finite economy

(1)

2.3.3 Archival expansion: An economy with Turing machine components

(1)

2.3.4 Conditional forecasting: Economies with universal machine components

(1)

2.3.5 Undecidability propositions

(1)

2.3.6 General comments

(3)

2.4 Social welfare evaluations

(7)

2.4.1 The decision setting

(3)

2.4.2 The political process

(1)

2.4.3 The computability of a political program

(2)

2.4.4 Predictability of restricted programs

(1)

2.5 Conclusions

(5)

Appendix: Proof of Theorem 2.5

103

(2)

3 Microeconomic Foundations of Cyclical Irregularities or "Chaos"

105

(32)

3.1 Introduction

105

(1)

3.2 The research problem

106

(8)

3.2.1 The meaning of "chaos" in dynamic systems

107

(3)

3.2.2 Nonlinearities and underlying microeconomic interactions

110

(4)

3.3 A model of microeconomic interaction

114

(13)

3.3.1 Specification of interaction neighborhoods

114

(2)

3.3.2 Specification of interaction conventions

116

(1)

3.3.3 Simulation of firm behavior

117

(1)

3.3.4 Classification of simulated time series

118

(7)

3.3.5 Preliminary indications

125

(2)

3.4 Interpretations

127

(8)

3.4.1 The background model

127

(4)

3.4.2 The computation irreducibility hypothesis

131

(1)

3.4.3 Reexamination of economic implications

131

(4)

3.5 Extensions and applications

135

(2)

4 Qualitative Effects of Monetary Policy in "Rich" Dynamic Systems

137

(20)

4.1 Introduction

137

(1)

4.2 The experimental setting

138

(2)

4.3 Complexity classification of dynamic behaviors

140

(9)

4.3.1 Qualitative types of dynamic behavior

140

(7)

4.3.2 Projective properties

147

(1)

4.3.3 Modeling considerations

148

(1)

4.3.4 Dynamics and expectations

148

(1)

4.3.5 Industry structure

149

(1)

4.4 Policy interventions

149

(6)

4.4.1 Simulating monetary interventions

151

(4)

4.4.2 Properties of the system and experimental protocols

155

(1)

4.5 Results and preliminary interpretations

155

(2)

4.5.1 Incomplete stabilization

156

(1)

4.5.2 Economic implications

156

(1)

5 Decentralized, Dispersed Exchange without an Auctioneer: A Simulation Study

157

(24)

5.1 Introduction

157

(1)

5.2 A model of dispersed exchange

158

(3)

5.2.1 Endowments and utilities

159

(1)

5.2.2 Advertising neighborhoods, information costs, and trade protocol: The rules of the game

159

(2)

5.3 Strategies of agents

161

(5)

5.3.1 Boundedly rational agents of fully rational players

161

(1)

5.3.2 Truthful disclosure

162

(1)

5.3.3 The agent's computational capacity

162

(1)

5.3.4 The candidate algorithm

163

(1)

5.3.5 The expected gain from signaling

163

(1)

5.3.6 Estimating the likelihood of neighbor actions

164

(1)

5.3.7 Simulation procedures

165

(1)

5.3.8 The coefficient of resource utilization

166

(1)

5.4 Simulation results

166

(3)

5.4.1 Reporting format

166

(1)

5.4.2 Illustrative results

167

(1)

5.4.3 Trader accounts

168

(1)

5.4.4 Comment

169

(1)

5.4.5 A second illustrative example

169

(1)

5.5 Information cost and efficiency

169

(5)

5.5.1 Interactions of advertising cost and neighborhood size

170

(1)

5.5.2 Interpretations

171

(3)

5.6 Concluding comments

174

(7)

6 Approximations of Cooperative Equilibria in Multiperson Prisoners' Dilemma Played by Cellular Automata

181

(29)

6.1 Introduction

181

(2)

6.2 The model

183

(7)

6.2.1 Subgame and sub-subgame structure of MPD

183

(5)

6.2.2 Threshold conditions for equilibria in repeated play

188

(2)

6.3 Strategic equivalence and the complexity of cellular automation rules

190

(2)

6.3.1 Digression: Study of cellular automaton complexity properties

190

(2)

6.4 The complexity of bounded-rationality forms

192

(5)

6.4.1 Classes of strategic equivalence in multiperson games

193

(4)

6.5 A theorem on "Nash-like" equilibria in MPD

197

(1)

6.6 A "Nash-like" solution to MPD

198

(6)

6.7 Conclusions

204

(1)

Appendix

205

(5)

7 The Complexity of Social Groups and Social Systems Described by Graph Structures

210

(33)

7.1 Introduction

210

(3)

7.2 Directed graphs and their representation: An overview

213

(18)

7.2.1 Arbitrary system functions: "Structure generators"

216

(2)

7.2.2 Analysis of the undirected graph

218

(1)

7.2.3 Parameters of the undirected graph

218

(1)

7.2.4 The function "rumor transmission with recorded path"

218

(4)

7.2.5 Complexity of the rumor propagating machine

222

(9)

7.3 The directed graph

231

(10)

7.3.1 The graph that is less than total

231

(4)

7.3.2 Complexity measurement for the directed graph

235

(1)

7.3.3 Case example: Complexity of organizational structures

236

(5)

7.4 Conclusion

241

(2)

Works Cited

243

(8)

Index

251

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Barriers and Bounds to Rationality

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Table of Contents

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