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Service Level Agreements (SLAs) have obvious value for Service-Oriented Computing and have received attention from both academics and industry. However, SLAs still lack a theoretical basis and effective techniques to facilitate automatic SLA establishment. In this paper, we classify negotiations into four types, and focus on the 1-to-1 Web services negotiation between a single service provider and a single service consumer. We make three contributions. Firstly, we represent the 1-to-1 Web services negotiation as a bargaining game. Here, we are interested in a bargain that takes into account the interests of both a service provider and a service consumer, in other words, a fair solution. Secondly, we determine a Nash equilibrium that can be regarded as the fair solution to a two-player bargaining game. We also determine the fair solution to the 1-to-1 Web services negotiation. Finally, we discuss issues that may arise with the 1-to-1 Web services negotiation under credible threats, incomplete information, time constraints, and multiple attributes.