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In many social and biological systems agents simultaneously and adaptively compete for limited resources, thereby altering their environment. We analyze a simple model that incorporates fundamental features of such systems. If the space of strategies available to the agents is small, the system is in a phase in which all information available to the agents' strategies is traded away, and agents' choices are maladaptive, resulting in a poor collective utilization of resources. For larger strategy spaces, the system is in a phase in which the agents are able to coordinate their actions to achieve a better utilization of resources. The best utilization of resources occurs at a critical point, when the dimension of the strategy space is on the order of the number of agents. [S0031-9007(99)08619-6]

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We present a new method for analyzing time series which is designed to extract inherent deterministic dependencies in the series. The method is particularly suited to series with broad-band spectra such as chaotic series with or without noise. We derive quantities, ~j(e), based on conditional probabilities, whose magnitude, roughly speaking, is an indicator of the extent to which the kth element in the series is a deterministic function of the (k-j)th element to within a measurement uncertainty, e. We apply our method to a number of deterministic time series generated by chaotic processes such as the tent, logistic and H~non maps, as well as to sequences of quasi-random numbers. In all cases the 6j correctly indicate the expected dependencies. We also show that the ~j are robust to the addition of substantial noise in a deterministic process. In addition, we derive a predictability index which is a measure of the extent to which a time series is predictable given some tolerance, e. Finally, we discuss the behavior of the 6i as e approaches zero.

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