## 3 Demand-Response Aggregator Frameworks in Future US Electricity Markets
### Deterministic Game Theoretical Prosumer-Aggregator Frameworks  
To enjoy the benefits of market-based DR, market presence in modeling is substantial for DR aggregator frameworks. However, some frameworks like [206; 207] consider a non-profitable utility/aggregator (lack of competition) without market access. Both papers assume the deterministic modeling of aggregators and prosumers, ignoring the effect of several uncertainties. At the same time, Ref. [206] proposes a framework with some level of flexibility since prosumer battery models are considered, while Ref. [207] proposes an auction-like process run by a utility with multiple aggregators splitting the rewards but without any consideration of prosumer flexibility. However, Ref. [207] is a good starting point for the derivation of closed-form game-theoretic strategies in DR aggregator frameworks. Prosumer privacy or framework scalability are out of the scope of these studies. Modeled competition between the DR aggregator and the prosumer can be found in other works like [208], which considers market access but not uncertainty or any particular prosumer flexibility options (no HEMS/BEMS constraints). Prosumer privacy and framework scalability with the number of prosumers and constraints are out of the scope of this work. However, this work is another excellent example of Stackelberg bottom-up pure strategy extraction, with full mathematical proofs provided. Some other Stackelberg competition frameworks with selfish players but without uncertainty include [73; 74; 209], where a degree of flexibility is assumed through prosumer time-coupling constraints on the total desired daily traded energy. Moreover, in the same works, the authors have considered prosumer privacy by developing a decentralized solution that does not require sharing any HEMS/BEMS details (objective, constraints, devices, preferences, settings, PI data, etc.) with the DR aggregator. The same decentralized solution allows for scalability with the number of prosumers, while the strategies and computational complexities are rigorously derived. Other game-theoretic competition frameworks, like [210], show a different degree of flexibility by adding budget constraints for the prosumers and considering multiple utilities (no market). Uncertainty is not part of this study; however, a degree of privacy is obtained based on the prosumers' sharing of optimal decisions, and a degree of scalability is attained from the distributed nature of the algorithm, but for convex games only. Another degree of flexibility is that of bidirectional energy flow between DR aggregators and prosumers. As many frameworks [207; 208; 210; 211] do not allow this, we identify that some other works, like [73; 74; 204; 209], allow for energy to flow bidirectionally between the prosumer, the DR aggregator, and the market, resulting in either selling energy to the market or buying energy from the market, achieving new levels of monetary rewards, as explained in [74; 209]. Please note that in the case of [204], a bidirectional energy formulation is offered, but the proposed solution only solves the unidirectional energy flow problem. Moreover, Ref. [204] does not consider any uncertainty, prosumer privacy, or scalability of the solution as part of the scope of their research. A final example of framework flexibility is the prosumer's behavioral heterogeneity, which includes different objectives and constraints, includingdifferences in prosumer sector (residential, commercial, or industrial) [212], or allowing for elasticity to be evaluated for each prosumer separately [74; 209]. Although this deterministic game-theoretic framework review on Stackelberg games may not be fully exhaustive, the key takeaway is the evaluation criteria used in this framework and all subsequent sections, which are one of the main contributions of this paper. Apart from DR applications, Stackelberg games have also been used for energy storage aggregators [213], cybersecurity [214], and road network checkpoints around the LAX airport (ARMOR program) [215].