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Market mechanisms have been suggested in the last few years as a tool for allocating shared networks resources among several competing users. In this paper, we consider the efficiency loss of such mechanisms in the presence of a large number of users. We model the user interactions as a game with a heterogeneous population of players characterized by random utility functions. If the utility functions are bounded, then the non-cooperative equilibrium are nearly as efficient as the social optimum with high probability when the number of users is large. This efficiency result holds for a single link with a fixed or an increasing capacity. Using a standard probabilistic analysis, we show that the efficiency loss incurred by the market mechanism decreases almost exponentially in the number of users. If, however, the utility functions are not bounded, then the loss of efficiency does not converge to zero. We also provide results for networks by sampling the users at random based on their paths.