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arXiv2026

Incentive-Aligned Vehicle-to-Vehicle Energy Trading via Nash-Integrated Multi-Agent Reinforcement Learning

Vehicle-to-vehicle (V2V) energy trading enables decentralized peer-to-peer energy exchange among electric vehicles (EVs), reducing grid dependency while monetizing surplus capacity. However, coordinating self-interested EV agents with diverse charging needs and uncertain arrival-departure schedules remains challenging. Existing approaches either require centralized optimization with computational limitations or lack fairness guarantees. This paper integrates Nash Bargaining Solution into Multi-Agent Deep Deterministic Policy Gradient, namely Nash-MADDPG, for incentive-aligned V2V energy trading. Nash bargaining determines efficient bilateral pricing, while Nash-guided price proximity rewards align agent learning toward bargaining-optimal strategies. Evaluation over 30-day continuous operation demonstrates an improvement of 61.6% in social welfare and 62.9% improvement in trading volume over Double Auction, while achieving superior fairness, such as 40.1% improvement in Jain's index. Testing across 6-100 agents over a 30-day horizon with continuous vehicle turnover confirms scalability across population size and empirically stable pricing near the Nash Bargaining benchmark.

math.OC↗

arXiv2020

Some topological properties of topological rough groups

Let $(U, R)$ be an approximation space with $U$ being non-empty set and $R$ being an equivalence relation on $U$, and let $\overline{G}$ and $\underline{G}$ be the upper approximation and the lower approximation of subset $G$ of $U$. A topological rough group $G$ is a rough group $G=(\underline{G}, \overline{G})$ endowed with a topology, which is induced from the upper approximation space $\overline{G}$, such that the product mapping $f: G\times G\rightarrow \overline{G}$ and the inverse mapping are continuous. In the class of topological rough groups, the relations of some separation axioms are obtained, some basic properties of the neighborhoods of the rough identity element and topological rough subgroups are investigated. In particular, some examples of topological rough groups are provided to clarify some facts about topological rough groups. Moreover, the version of open mapping theorem in the class of topological rough group is obtained. Further, some interesting open questions are posed.

math.GN↗