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A Binary-Agent-Resource (B-A-R) model [1,2] consisting of N agents competing for resources
described by a resource level 1/2 L < 1, where L = Y/N with Y being the maximum amount of
resource per turn for the agents, is studied numerically and analytically. The agents may or may
not be networked for information sharing. It is found that the outcome time series, which gives the
winning action and consists of zeros and ones for B-A-R models, show transitions from one pattern
to another as the resource level L varies. The number of different patterns (for 1/2 L < 1)
depends on the size of the strategy space. Each state is characterized by a unique pattern in the
outcome time series and an average success rate. The highest success rate, representing that of
the richest agents in the game, for given L is a simple fraction corresponding to the fraction of 1's
in the pattern specified by L. Analytically, results of microscopic approach based on the decision
dynamics of the agents and macroscopic approach based on the evolution in the history space are
in excellent agreement with results of numerical simulations. The critical resource level values
L for transitions from one pattern to another are derived, with results in good agreements with
c
simulations. Results in networked population [3] will be compared with those in non-networked
population.
[1] N.F. Johnson and P.M. Hui, preprint cond-mat/0306516. [2] N.F. Johnson, P.M. Hui, D. Zheng, and C.W. Tai, Physica A 269, 493 (1999). [3] S. Gourley, S.C. Choe, N.F. Johnson, and P.M. Hui, preprint cond-mat/0401527. |