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We study the problem of allocating shared resources, such as bandwidth in computer networks and computational resources in shared clusters, among multiple users by the proportional-share market mechanism. Under this mechanism, each user partitions his budget among the multiple resources and receives a fraction of each resource proportional to his bid. We first formulate the resource allocation game under the proportional-share mechanism and study the efficiency and fairness of the equilibrium in this game. We present analytic and simulation results demonstrating that the proportional-share mechanism achieves a reasonable balance of high degrees of efficiency and fairness at the equilibrium.