We study a resource utilization scenario characterized by intrinsic attractiveness , in a system of many restaurants where customers compete  to get the best services out of many choices  . Results for the case with uniform attractiveness are reported. When attractiveness is uniformly distributed, it gives rise to a Zipf-Pareto law for the number of customers. We perform an exact calculation for the utilization fraction for the case when choices are made independent of attractiveness. A variant of the model is also introduced where the attractiveness can be treated as a fitness to stay in the business. When a restaurant loses customers, its fitness is replaced by a random fitness. The  fitness distribution is characterized by a power law, but the power law distribution in number of customers still holds , implying the robustness of the model. Our model serves as a paradigm for city size distribution and the emergence of Zipf law.
We study a resource utilization scenario characterized by intrinsic attractiveness . We consider a system of many restaurants where customers compete , as in a game, to get the best services out of many choices using iterative learning . Results for the case with uniform attractiveness are reported. When attractiveness is uniformly distributed, it gives rise to a Zipf-Pareto law for the number of customers. We perform an exact calculation for the utilization fraction for the case when choices are made independent of attractiveness. A variant of the model is also introduced where the attractiveness can be treated as a fitness to stay in the business. When a restaurant loses customers, its fitness is replaced by a random fitness. The steady state fitness distribution is characterized by a power law, but the distribution in number of customers is still given by power law , implying the robustness of the model. Our model serves as a paradigm for city size distribution and the emergence of Zipf law.
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, in
. We consider
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, as in a game,
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using iterative learning
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steady state
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power law
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still holds
is still given by power law