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Reliable access to electricity is still a challenge in many developing countries. Indeed, rural areas in sub-Saharan Africa and developing countries such as India still encounter frequent power outages. Local energy markets (LEMs) have emerged as a low-cost solution enabling prosumers with power supply systems such as solar PV to sell their surplus of energy to other members of the local community. This paper proposes a one-to-one automated negotiation framework for peer-to-peer (P2P) local trading of electricity. Our framework uses an autonomous agent model to capture the preferences of both an electricity seller (consumer) and buyer (small local generator or prosumer), in terms of price and electricity quantities to be traded in different periods throughout a day. We develop a bilateral negotiation framework based on the well-known Rubinstein alternating offers protocol, in which the quantity of electricity and the price for different periods are aggregated into daily packages and negotiated between the buyer and seller agent. The framework is then implemented experimentally, with buyers and sellers adopting different negotiation strategies based on negotiation concession algorithms, such as linear heuristic or Boulware. Results show that this framework and agents modelling allow prosumers to increase their revenue while providing electricity access to the community at low cost. [ABSTRACT FROM AUTHOR]