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To support users\u2019 privacy management, we propose a novel agent-based negotiation framework to negotiate privacy permissions between users and service providers using a new multi-issue alternating-offer protocol based on exchanges of partial and complete offers. Additionally, we introduce a novel approach to learning users\u2019 preferences in negotiation and present two variants of this approach: one variant personalised to each individual user, and one personalised depending on the user\u2019s privacy type. To evaluate them, we perform a user study with participants, using an experimental tool installed on the participants\u2019 mobile devices. We compare the take-it-or-leave-it approach, in which users are required to accept all permissions requested by a service, to negotiation, which respects their preferences. Our results show that users share personal data 2.5 times more often when they are able to negotiate while maintaining the same level of decision regret. Moreover, negotiation can be less mentally demanding than the take-it-or-leave-it approach and it allows users to align their privacy choices with their preferences. 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