Robert M Axelrod, The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration, Princeton studies in complexity (Princeton, N.J: Princeton University Press, 1997).
This book builds upon Axelrod's earlier work on cooperation--specifically using the Prisoner's Dilemma--by adding complexity to the mix. "Adding complexity to that framework allows the exploration of many interesting and important features of competition and collaboration that are beyond the reach of the Prisoner's Dilemma paradigm" (3).
"Complexity theory involves the study of many actors and their interactions. The actors may be atoms, fish, people, organizations or nations...a primary tool of complexity theory is computer simulation" (3).
"Agent-based modeling is a third way of doing science. Like deduction, it starts with a set of explicitly assumptions. But unlike deduction, it does not prove theorems. Instead, an agent-based model generates simulated data that can be analyzed inductively. Unlike typical induction, however, the simulated data come from a rigorously specified set of rules rather than direct measurement of the real world. Whereas the purpose of induction is to find patterns in data and that of deduction to find consequences of assumptions, the purpose of agent-based modeling is to aid intuition" (3-4).
Tuesday, March 2, 2010
Monday, March 1, 2010
Boulding: General Systems Theory: The Skeleton of Science
Boulding, Kenneth E. 1956. “General Systems Theory-The Skeleton of Science.” Management Science 2(3) (April): 197-208.
“General Systems Theory is a name which has come into use to describe a level of theoretical model-building which lies somewhere between the highly generalized constructions of pure mathematics and the specific theories of the specialized disciplines” 197
“The objectives of General Systems Theory…can be set out with varying degrees of ambition and confidence. At a low level of ambition but with a high degree of confidence it aims to point out similarities in the theoretical constructions of different disciplines, where these exist, and to develop theoretical models having applicability to at least two different fields of study. A t a higher level of ambition, but with perhaps a lower degree of confidence it hopes to develop something like a ‘spectrum’ of theories—a system of systems which may perform the function of a ‘gestalt’ in theoretical construction. Such ‘gestalts’ in special fields have been of great value in directing research towards the gaps which they reveal” 198
Two possible approaches to GST: Find common phenomenon to different schools of theory: an individual interacting with an environment, growth, information/communication, etc. Or, you could create a framework for mapping out the interaction of different theories across degrees of complexity.
“General Systems Theory is a name which has come into use to describe a level of theoretical model-building which lies somewhere between the highly generalized constructions of pure mathematics and the specific theories of the specialized disciplines” 197
“The objectives of General Systems Theory…can be set out with varying degrees of ambition and confidence. At a low level of ambition but with a high degree of confidence it aims to point out similarities in the theoretical constructions of different disciplines, where these exist, and to develop theoretical models having applicability to at least two different fields of study. A t a higher level of ambition, but with perhaps a lower degree of confidence it hopes to develop something like a ‘spectrum’ of theories—a system of systems which may perform the function of a ‘gestalt’ in theoretical construction. Such ‘gestalts’ in special fields have been of great value in directing research towards the gaps which they reveal” 198
Two possible approaches to GST: Find common phenomenon to different schools of theory: an individual interacting with an environment, growth, information/communication, etc. Or, you could create a framework for mapping out the interaction of different theories across degrees of complexity.
Simon: The Architecture of Complexity
Simon, Herbert A. 1962. “The Architecture of Complexity.” Proceedings of the American Philosophical Society 106(6) (December 12): 467-482.
“Roughly, by a complex system I mean one made up of a large number of parts that interact in a nonsimple way. In such systems, the whole is more than the sum of the parts, not in an ultimate, metaphysical sense, but in the important pragmatic sense that, given the properties of the parts and the laws of their interaction, it is not a trivial matter to infer the properties of the whole” (468).
“Thus, the central theme that runs through my remarks is that complexity frequently takes the form of hierarchy, and that hierarchic systems have some common properties that are independent of their specific content. Hierarchy, I shall argue, is one of the central structural schemes that the architect of complexity uses” (468).
“By a hierarchic system, or hierarchy, I mean a system that is composed of interrelated sub-systems, each of the latter being, in turn, hierarchic in structure until we reach some lowest level of elementary subsystem” (468).
“There is one important difference between the physical and biological hierarchies, on the one hand, and social hierarchies, on the other. Most physical and biological hierarchies are described in spatial terms…On the other hand, we propose to identify social hierarchies not by observing who lives close to whom but by observing who interacts with whom. These two points of view can be reconciled by defining hierarchy in terms of intensity of interaction” (469).
“We have shown thus far that complex systems will evolve from simple systems much more rapidly if there are stable intermediate forms than if there are not. The resulting complex forms in the former case will be hierarchic. We have only to turn the argument around to explain the observed predominance of hierarchies among the complex systems nature presents to us” (473).
“In hierarchic systems, we can distinguish between the interactions among subsystems, on the one hand, and the interactions within subsystems…The interactions at the different levels may be, and often will be, of different orders of magnitudes” (473-4).
“At least some kinds of hierarchic systems can be approximated successfully as nearly decomposable systems. The main theoretical findings from the approach can be summed up in two propositions: (a) in a nearly decomposable system, the short-run behavior of each of the component subsystems is approximately independent of the short-run behavior of the other components; (b) in the long run, the behavior of any one of the components depends in only an aggregate way on the behavior of the other components” (474).
“How complex or simple a structure is depends critically upon the way in which we describe it. Most of the complex structures round in the world are enormously redundant, and we can use this redundancy to simplify their description. But to use it, to achieve the simplification, we must find the right representation” (481).
“My thesis has been that one path to the construction of a non-trivial theory of complex systems is by way of a theory of hierarchy. Empirically, a large proportion of the complex systems we observe in nature exhibit hierarchic structure. On theoretical grounds we could expect complex systems to be hierarchies in a world in which complexity had to evolve from simplicity. In their dynamics, hierarchies have property, near-decomposability, that greatly simplifies their behavior. Near-decomposability also simplifies the description of a complex system, and makes it easier to understand how the information needed for the development or reproduction of the system can be stored in reasonable compass” (481-2).
“Roughly, by a complex system I mean one made up of a large number of parts that interact in a nonsimple way. In such systems, the whole is more than the sum of the parts, not in an ultimate, metaphysical sense, but in the important pragmatic sense that, given the properties of the parts and the laws of their interaction, it is not a trivial matter to infer the properties of the whole” (468).
“Thus, the central theme that runs through my remarks is that complexity frequently takes the form of hierarchy, and that hierarchic systems have some common properties that are independent of their specific content. Hierarchy, I shall argue, is one of the central structural schemes that the architect of complexity uses” (468).
“By a hierarchic system, or hierarchy, I mean a system that is composed of interrelated sub-systems, each of the latter being, in turn, hierarchic in structure until we reach some lowest level of elementary subsystem” (468).
“There is one important difference between the physical and biological hierarchies, on the one hand, and social hierarchies, on the other. Most physical and biological hierarchies are described in spatial terms…On the other hand, we propose to identify social hierarchies not by observing who lives close to whom but by observing who interacts with whom. These two points of view can be reconciled by defining hierarchy in terms of intensity of interaction” (469).
“We have shown thus far that complex systems will evolve from simple systems much more rapidly if there are stable intermediate forms than if there are not. The resulting complex forms in the former case will be hierarchic. We have only to turn the argument around to explain the observed predominance of hierarchies among the complex systems nature presents to us” (473).
“In hierarchic systems, we can distinguish between the interactions among subsystems, on the one hand, and the interactions within subsystems…The interactions at the different levels may be, and often will be, of different orders of magnitudes” (473-4).
“At least some kinds of hierarchic systems can be approximated successfully as nearly decomposable systems. The main theoretical findings from the approach can be summed up in two propositions: (a) in a nearly decomposable system, the short-run behavior of each of the component subsystems is approximately independent of the short-run behavior of the other components; (b) in the long run, the behavior of any one of the components depends in only an aggregate way on the behavior of the other components” (474).
“How complex or simple a structure is depends critically upon the way in which we describe it. Most of the complex structures round in the world are enormously redundant, and we can use this redundancy to simplify their description. But to use it, to achieve the simplification, we must find the right representation” (481).
“My thesis has been that one path to the construction of a non-trivial theory of complex systems is by way of a theory of hierarchy. Empirically, a large proportion of the complex systems we observe in nature exhibit hierarchic structure. On theoretical grounds we could expect complex systems to be hierarchies in a world in which complexity had to evolve from simplicity. In their dynamics, hierarchies have property, near-decomposability, that greatly simplifies their behavior. Near-decomposability also simplifies the description of a complex system, and makes it easier to understand how the information needed for the development or reproduction of the system can be stored in reasonable compass” (481-2).
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