Strategic and Fair Aggregator Interactions in Energy Markets: Multi-Agent Dynamics and Quasiconcave Games

The introduction of aggregator structures has proven effective in bringing fairness to energy resource allocation by negotiating for more resources and economic surplus on behalf of users. This paper extends the fair energy resource allocation problem to a multi-agent setting, focusing on interactions among multiple aggregators in an electricity market. We consider a setting where aggregators submit quantity-only bids as in a noncooperative Cournot game. Unlike classical Cournot models, where firms optimize only for profit, our framework incorporates a bi-level decision process, in which each aggregator determines its total purchase while simultaneously optimizing the internal allocation among its users based on fairness-efficiency trade-off objectives and constraints. We prove that the strategic optimization problems faced by the aggregators form a quasi-concave game, ensuring the existence of a Nash equilibrium. This resolves complexities related to market price dependencies on total purchases and balancing fairness and efficiency in energy allocation. In addition, we design simulations to characterize the equilibrium points of the induced game, demonstrating how aggregators stabilize market outcomes, ensure fair resource distribution, and optimize user surplus. Our findings offer a robust framework for understanding strategic interactions among aggregators, contributing to more efficient and equitable energy markets.