## 3 Demand-Response Aggregator Frameworks in Future US Electricity Markets  
### Competition in the Prosumer-Aggregator Frameworks  
An overview of aggregator or prosumer frameworks categorized by methods, objectives, and devices compatible with that framework are presented in Table 6 for the day-ahead and imbalance markets (IM) and for the intra-day (IDM), reserve, and congestion markets equivalently. These frameworks consider specific devices only and optimize either the aggregator's or the prosumer's costs, but not both simultaneously; therefore, the underlying competition between the prosumers and the aggregator is neglected (open research question about competition in Section 3.7). This gap around competition is one of the five evaluation criteria summarized in Section 3.7, and it can be overcome with game-theoretic methods, which are analyzed later in this section, where all players are optimized while device models may or may not be considered. In the second case, some energy management systems from the prosumer's side are assumed. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Market Type** & **Method** & \begin{tabular}{l} **Objective: Min** \\ **Agg./Pros. Cost** \\ \end{tabular} & \begin{tabular}{l} **Devices** \\ \end{tabular} & \
\begin{tabular}{l} **Prosumer Reward** \\ \end{tabular} &
\begin{tabular}{l} **Paper** \\ \end{tabular} \\ \hline DAM & Linear Optimization & ✓ /- & Appliances & - & [111] \\ MILP & ✓ /- & BESS, appliances & Time-varying & [140] \\ MILP & ✓ /- & Appliances & Optimal flat rate & [141] \\ MILP & -/✓ & BESS, appliances & TOU, CPP, RTP & [142] \\ MILP & -/✓ & Appliances & TOU, time-varying & [143] \\ Bi-level Optimization & ✓ /- & EV & - & [144] \\ Bi-level Stochastic Opt. & ✓ /- & EV & - & [144] \\ Stochastic Robust Opt. & ✓ /- & EV & - & [145] \\ Stochastic Robust Opt. & -/✓ & Appliances & RTP & [146] \\ Robust Optimization & ✓ /- & EV & - & [147] \\ Robust Optimization & ✓ /- & BESS, thermal loads - & [148] \\ Optimization & ✓ /- & Electric heaters & Flat rate, extra & [149] \\ Algorithm & -/✓ & BESS, appliances & RTP & [150] \\ Algorithm & ✓ /- & EV & - & [151] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Overview of DR aggregator frameworks for the DAM, IDM, and reserve markets (aFRR, FCR, and mFRR). The star \(\surd{}^{*}\) denotes an imbalance type of cost for the aggregator. The optimization of either the aggregator’s or the prosumer’s objective indicates a significant lack of competition consideration when modeling aggregator-prosumer frameworks. The literature often models the demand side (prosumer) separately from the supply side (aggregator). For example, Ref. [187] focuses only on the prosumer side, ignoring the presence of an aggregator and the competition between them. These approaches lead to suboptimal solutions because the players (prosumers or aggregators) have a wrong or no perception of the underlying competition. Game theory can model existing market competition and, therefore, derive optimal strategies that maximize the payoffs of all selfish players of the energy trading game. In the case of the prosumer-aggregator, the aggregator firm has the freedom to set up its own competition model for its prosumers, as long as it is able to market it properly and convince the prosumers to register. The market operator (independent system operator, also known as ISO) requires metering infrastructure to be in place so that it is able to monitor actions that are unfair to the market, such as hiding true capacities, bidding significantly lower quantities than the nominal capacity, etc. The most common types of competition with respect to homogeneous products in markets are Stackelberg, Cournot, and Bertrand. Stackelberg games have a leader-follower structure, where the leader firm (firm with the most market power) plays first with an