We study network and congestion games with atomic players that can split their flow. This type of games readily applies to competition among freight companies, telecommunication network service providers, intelligent transportation systems and manufacturing with flexible machines. We analyze the worst-case inefficiency of Nash equilibria in those games and conclude that although self-interested agents will not in general achieve a fully efficient solution, the loss is not too large. We show how to compute several bounds for the worst-case inefficiency, which depend on the characteristics of cost functions and the market structure in the game. In addition, we show examples in which market aggregation can adversely impact the aggregated competitors, even though their market power increases. When the market structure is simple enough, this counter-intuitive phenomenon does not arise.