Negotiation plays a fundamental role in shaping human societies, underpinning conflict resolution, institutional design, and economic coordination. This article introduces E³-MAN, a novel multi-agent model for negotiation that integrates individual utility maximization with fairness and institutional legitimacy. Unlike classical approaches grounded solely in game theory, our model incorporates Bayesian opponent modeling, transfer learning from past negotiation domains, and fallback institutional rules to resolve deadlocks. Agents interact in dynamic environments characterized by strategic heterogeneity and asymmetric information, negotiating over multidimensional issues under time constraints. Through extensive simulation experiments, we compare E³-MAN against the Nash bargaining solution and equal-split baselines using key performance metrics: utilitarian efficiency, Nash social welfare, Jain fairness index, Gini coefficient, and institutional compliance. Results show that E³-MAN achieves near-optimal efficiency while significantly improving distributive equity and agreement stability. A legal application simulating multilateral labor arbitration demonstrates that institutional default rules foster more balanced outcomes and increase negotiation success rates from 58% to 98%. By combining computational intelligence with normative constraints, this work contributes to the growing field of socially aware autonomous agents. It offers a virtual laboratory for exploring how simple institutional interventions can enhance justice, cooperation, and robustness in complex socio-legal systems.