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Decentralized algorithms are examined for optimally distributing a divisible resource in a distributed computer system. To study this problem in a specific context, the problem of optimal file allocation is considered. In this case, the optimization criteria include both the communication cost and average processing delay associated with a file access. The algorithms examined have their origins in the field of mathematical economics. They are shown to have several attractive properties, including their simplicity and distributed nature, the computation of feasible and increasingly better resource allocations as the result of each iteration, and, in the case of file allocation, rapid convergence. Conditions are formally derived under which the algorithms are guaranteed to coverage, and their convergence behavior is additionally examined through simulation.< >