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This paper considers optimization problems of energy demand networks including aggregators and investigates strategic behavior of the aggregators. The participants of the network are a utility company, who plays a role of energy supply source, aggregators and a large number of consumers. We suppose that the network will be optimized by price response based or, in other words, market based optimization processes. We also suppose that the aggregator has a strategic parameter in its cost function and, by choosing the parameter strategically, the aggregator will try to pursue its own benefit. This general problem formulation will apply to a specific problem setting, where the aggregator possess battery storage with different specifications: The one is high-performance and expensive and the other is low-performance and cheap. The aggregator will choose total capacity of storage to be installed and a ratio of high-performance storage to low-performance storage as the strategic parameters and try to increase its own benefit. By using numerical examples, we show that the strategic decision making by the aggregator could provide useful insights in qualitative analysis of energy demand networks.