In an era where renewable energy resources are increasingly integrated into our power systems, and consumer-centric approaches gain traction, local energy markets emerge as a pivotal mechanism for empowering prosumers. This paper presents a novel bilevel optimization model that uniquely blends the dynamics of peer--to--peer energy markets with the physical realities of power distribution networks. The innovation steems from introducing a tariff design approach based on affine functions to shape prosumer behavior towards operationally efficient and secure energy exchanges. This is critical as previous market designs often overlooked the physical constraints of power flows, leading to potential risks in voltage regulation and economic efficiency. The lower level of the model encapsulates the interactions among prosumers in a generalized Nash equilibrium problem (GNEP), modeling active and reactive power injections of prosumers. The upper level, representing the role of the distribution system operator, strategically computes tariffs to steer the market to an operationally efficient equilibrium. The paper relies on the classical Nikaido--Isoda (NI) reformulation to characterize the GNEP, a key aspect in leveraging a proof of strong stability of the lower--level solution. Computational experiments on various IEEE test feeder instances reveal the model’s capacity to efficiently align prosumer behavior with operational objectives, utilizing only the tariff information, thereby simplifying the decision-making process in complex distribution systems.