A family of self-organizing systems

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Cornell University, Center for Applied Mathematics, 1966 - Adaptive control systems - 106 pages
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An investigation was made of a class of adaptive systems and the systems' behaviors as game-playing machines. Each member of the class is described by a set of parameters that specifies its reenforcement mechanism. In general, such a mechanism tends to increase successful strategies' probabilities of occurrence. However, the parameters must be carefully selected if the adaptive system's probability of winning is to approach one. The paper first develops a class of urn models, described by the same parameters; and shows that each urn model behaves very much like a corresponding adaptive system. The familiar urns of Polya and Barnard Friedman are members of this class. Other members exhibit much more interesting behaviors. The paper analyzes the urn models and proves a sufficient condition for convergence to one, with probability one, of the right-ball ratio. It exhibits numerical results showing that, for practical applications, the condition is also necessary. Finally, it analyzes the glitch phenomenon. (Author).

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