In this paper we formulate the fixed budget resource allocation game to understand the performance of a distributed market-based resource allocation system. Multiple users decide how to distribute their budget bids) among multiple machines according to their individual preferences to maximize their individual utility. We look at both the efficiency and the fairness of the allocation at the equilibrium, where fairness is evaluated through the measures of utility uniformity and envy-freeness. We show analytically and through simulations that despite being highly decentralized, such a system converges quickly to an equilibrium and unlike the social optimum that achieves high efficiency but poor fairness, the proposed allocation scheme achieves a nice balance of high degrees of efficiency and fairness at the equilibrium.