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

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