Competition With Atomic Users

We study the efficiency of oligopoly equilibria in a model where firms compete over prices. The motivating examples are the allocation of network flows in a communication network or of traffic in a transportation network. Contrary to most related papers, we study the case when the users are atomic, i.e., each user controls a non-negligible fraction of the total traffic. We show that competition among profit maximizing firms can reduce the overall efficiency of the system, measured as the difference between users´ willingness to pay and delay costs. In particular, we characterize a tight bound of 1 - N / 6(N+1) worst case efficiency in pure strategy equilibria, where N is the number of atomic users.