In the classical Cournot model, each firm tries to maximize its own payoff by deciding an optimal strategy for determining the quantity of goods produced during each time period-i.e. turn, of the game. In the typical application, all firms compete in the same market. In more recent economic models, firms compete across a number of markets simultaneously. In this situation, a Networked Cournot Competition (NCC) graph models the relationship between firms and markets. This paper describes a model of competition among demand response aggregators (DRAs) as firms to sell energy (as a homogeneous good) stored in aggregated residential batteries in a networked environment where market constraints are effected and trades are generally facilitated through the actions of a market maker who's turn is sequentially distinct from the other players. We call this game Networked Stackelberg Competition (NSC). The impact of strategic anticipative behavior in networked markets is of paramount importance in distinguishing NSC from other competition models. For each firm, the optimal bidding strategy and Nash equilibrium are obtained through analyses of in an incomplete-information game. DRAs submit quantity bids and the market maker (system operator) controls the transaction power and transaction price over the network subject to transmission constraints and other market policies. Criteria required for existence of uniqueness of a Nash equilibrium are presented, and effectiveness of the game is also studied in the paper demonstrating demand response scheduling improves market situations. The details are presented in the application of a NSC model to real world case study data taken from the island of Maui, Hawaii.