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9780691026763

Barriers and Bounds to Rationality

by Albin, Peter S.; Foley, Duncan K.
  • ISBN13:

    9780691026763

  • ISBN10:

    0691026769

  • Format: Hardcover
  • Copyright: 1998-04-06
  • Publisher: Princeton Univ Pr

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Summary

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.

Table of Contents

Preface xiii(20)
Acknowledgments xxxiii
1 Introduction
3(70)
1.1 Dynamical systems
3(14)
1.1.1 Linear dynamical systems
4(3)
1.1.2 Nonlinear dynamical systems
7(8)
1.1.3 Cellular automata as models of nonlinear dynamical systems
15(2)
1.2 Dynamical systems in social and physical science
17(6)
1.2.1 Local and global interaction
18(1)
1.2.2 Topology and geometry in physical and social models
18(2)
1.2.3 Time and causality
20(1)
1.2.4 Identity and diversity
21(2)
1.3 Economic models of fully rational behavior
23(17)
1.3.1 The rational choice program
23(2)
1.3.2 Individual decision models-intertemporal optimization
25(1)
1.3.3 The finite-horizon Ramsey problem
25(3)
1.3.4 Market models
28(5)
1.3.5 Game theory models
33(7)
1.4 Definitions and measures of complexity
40(8)
1.4.1 Computational complexity
41(1)
1.4.2 Linguistic complexity
42(2)
1.4.3 Machine complexity
44(2)
1.4.4 Decidability, computational complexity, and rationality
46(1)
1.4.5 Dynamical systems and computational complexity
47(1)
1.5 Complexity in cellular automata
48(5)
1.5.1 Complexity types
50(2)
1.5.2 Computability, predictability, and complexity in cellular automata
52(1)
1.6 Modeling complex social and economic interactions
53(11)
1.6.1 Self-referencing individual agents
53(2)
1.6.2 Organizations
55(1)
1.6.3 Industries and economies
56(2)
1.6.4 Markets
58(3)
1.6.5 The local interaction multiperson Prisoners' Dilemma
61(3)
1.7 Complexity, rationality, and social interaction
64(4)
1.7.1 How complex are social systems?
65(2)
1.7.2 How smart do agents need to be?
67(1)
1.8 Toward a robust theory of action and society
68(5)
2 The Metalogic of Economic Predictions, Calculations, and Propositions
73(32)
2.1 Introduction
73(3)
2.2 Preliminaries: Automata and structural formations
76(7)
2.2.1 Finite automata
76(1)
2.2.2 Finite formations
77(2)
2.2.3 Generalized formations and finite surrogates
79(1)
2.2.4 General computation and computability
80(3)
2.3 Undecidability in generalized formations
83(8)
2.3.1 An economy with finite automaton components
84(1)
2.3.2 Structural properties of a finite economy
85(1)
2.3.3 Archival expansion: An economy with Turing machine components
85(1)
2.3.4 Conditional forecasting: Economies with universal machine components
86(1)
2.3.5 Undecidability propositions
87(1)
2.3.6 General comments
88(3)
2.4 Social welfare evaluations
91(7)
2.4.1 The decision setting
91(3)
2.4.2 The political process
94(1)
2.4.3 The computability of a political program
95(2)
2.4.4 Predictability of restricted programs
97(1)
2.5 Conclusions
98(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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