## 3 Demand-Response Aggregator Frameworks in Future US Electricity Markets
### Competition in the Prosumer-Aggregator Frameworks
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Market Type** & **Method** & **Objective: Min** & **Devices** & **Prosumer Reward** & **Paper** \\  & & **Agg./Pros.** & **Cost** & & \\ \hline DAM, IM & Linear Optimization & ✓/- & EV & - & [152] \\  & Linear Optimization & -/✓ & Storage heaters & RTP, fixed pay & [153] \\  & 2-Stage Stochastic Opt. & ✓/- & EV, TCL, appliances & - & [137] \\  & 2-Stage Stochastic Opt. & ✓/- & EV & Flat Rate & [154] \\  & 2-Stage Stochastic Opt. & ✓/- & EV & Yes & [155] \\  & 2-Stage Stochastic Opt. & ✓/- & BESS & Flat rate, extra & [156] \\  & Bi-level Stochastic Opt. & ✓/- & EV & Optimal flat rate & [157] \\  & Stochastic Optimization & ✓/- & Unspecified & Optimal time-varying & [158] \\ IDM & Linear Optimization & ✓/- & TCL & - & [159] \\  & MPC & ✓*/- & TCL & - & [160] \\ DAM, IDM & Probabilistic Opt. & ✓/- & BESS, appliances & - & [161] \\  & MPC, Simulation & ✓*/- & Space heaters & - & [162] \\ DAM, IDM, aFRR & 2-Stage Stochastic Opt. & ✓/- & EV & - & [163] \\ FCR & Simulation & ✓/- & Heat pumps & - & [164] \\ mFRR & Heuristic & -/✓ & TCL & - & [165] \\ aFRR & Agent-based & -/✓ & EV & Yes & [166] \\  & Multi-Objective Opt. & ✓/- & EV & - & [167] \\ DAM, aFRR & Optimization & ✓/- & EV & - & [168,169] \\  & Optimization & ✓/- & BESS & - & [170] \\  & Optimization & ✓/- & EV & - & [171] \\  & Optimization & ✓/- & EV & Degradation & [172] \\  & Optimization & ✓/- & EV & Flat rate & [173] \\  & Quadratic Optimization & ✓/- & EV & - & [174] \\  & 2-Stage Stochastic Opt. & ✓/- & EV & - & [175] \\  & 2-Stage Stochastic Opt. & ✓/- & EV, TCL & - & [176] \\  & Stochastic Optimization & ✓/- & EV, BESS & - & [177] \\  & MPC & ✓/- & EV, TCL & - & [178] \\  & MPC & ✓/- & Office HVAC & - & [179] \\ DAM, aFRR, IM & 2-Stage Stochastic Opt. & ✓/- & EV & - & [180] \\  & 2-Stage Stochastic Opt. & ✓/- & EV, TCL, appliances - & [181] \\  & 2-Stage Stochastic Opt. & ✓/- & EV & Optimal fixed & [182] \\ Congestion DAM & MILP & ✓/- & Appliances & RTP, time-varying & [183] \\ Cong. DAM/DSO & Linear Optimization & ✓/- & EV, heat pumps & Flat rate & [184] \\ tariffs & Linear Optimization & ✓/- & EV or appliances & - & [185,186] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _Cont._advantage and the followers observe the leader's action and respond appropriately. The optimal strategic response (highest payoff for all players) to the leader's Stackelberg action is a Stackelberg-type response from the followers. Stackelberg describes competition based on quantity [188]. A key advantage of Stackelberg models is that they often yield closed-form strategies, especially in full-information settings, making them analytically tractable and attractive for mechanism designs. However, their main limitation is the strong assumption of perfect information. In Cournot competition, players play simultaneously by competing for quantity (players with market power can affect the market price). Players can no longer observe others' actions, and this leads to different equilibria compared to the Stackelberg. Note that the leader in a Stackelberg competition can achieve at least the same or higher payoff as in the Cournot [189], which means that if the leader firm is in charge of the mechanism's design, it will choose a Stackelberg type of competition. Cournot equilibria can be more realistic than Stackelberg in electricity markets where aggregators or participants act independently and do not know the actions of others in advance. However, Cournot models often yield less efficient market outcomes and may be harder to solve analytically, especially with constraints. Bertrand competition describes the competition between multiple firms with respect to price. An ideal example of Bertrand competition could be the competition between multiple aggregators for the same prosumer, who would be offered multiple prices simultaneously for the same commodity (homogeneous product). In this case, Bertrand competition would result in marginal costs for the prosumer, which is a significant advantage.