In today’s society, aligning AI with social values is a major concern. Researchers are exploring various approaches to ensure AI systems adhere to human values, developing technologies that not only optimise performance but also promote social well-being. Traditional automated negotiation primarily focuses on agents optimising their individual outcomes. However, introducing social values, such as fairness, complicates the negotiation process as agents must balance personal gains with collective well-being and equitable outcomes. This paper presents initial research on developing negotiation strategies that prioritise both individual payoffs and social values. We explore the theory behind these strategies, propose initial models incorporating social values into utility functions, and present preliminary experimental results using simple use cases. Our experiments demonstrate that agents operating in social mode exhibit fairer behaviours, emphasising equitable outcomes over individual gain. Furthermore, our findings suggest several requirements for implementing our value-aware negotiation models, including the necessity for agents to have some information about others’ preferences, and a general commitment to social considerations. This paper represents our first steps towards more comprehensive solutions, with future work aimed at extending our investigations to more complex scenarios.