In this paper, we introduce a framework for studying the aggregated response for energy provision/consumption processes by distributed energy resources (DERs) that are physically connected to an electric power distribution network. In this framework, there is a set of agents referred to as aggregators that participate in a real-time energy market by submitting offers to sell, or bids to buy, a certain amount of energy at some price. To realize an offer or a bid, an aggregator interacts with a set of DERs and incentivizes them to produce (or consume) energy via some pricing strategy. In order to make a decision on whether or not to sell or buy energy, each DER uses the pricing information provided by the aggregator it is associated with, and some estimate of the average (or total) energy that neighboring DERs are willing to sell or buy, computed through some exchange of information among them through a cyber network; the topology of this cyber network is described by a connected undirected graph. The focus of this paper is on the DER strategic decision-making process, which we cast as a game with a single aggregator. In this context, we provide sufficient conditions on the aggregator's pricing strategy under which this game has a unique Nash equilibrium. Then, we propose a distributed algorithm that enables the DERs to seek this Nash equilibrium; this algorithm relies on simple computations using local information acquired through exchange of information with neighboring DERs. We illustrate our results through several numerical simulations.