Human societies have long used the capability of argumentation and dialogue to overcome and resolve conflicts that may arise within their communities. Today, there is an increasing level of interest in the application of such dialogue games within artificial agent societies. In particular, within the field of multi-agent systems, this theory of argumentation and dialogue games has become instrumental in designing rich interaction protocols and in providing agents with a means to manage and resolve conflicts. However, to date, much of the existing literature focuses on formulating theoretically sound and complete models for multi-agent systems. Nonetheless, in so doing, it has tended to overlook the computational implications of applying such models in agent societies, especially ones with complex social structures. Furthermore, the systemic impact of using argumentation in multi-agent societies and its interplay with other forms of social influences (such as those that emanate from the roles and relationships of a society) within such contexts has also received comparatively little attention. To this end, this paper presents a significant step towards bridging these gaps for one of the most important dialogue game types; namely argumentation-based negotiation (ABN). The contributions are three fold. First, we present a both theoretically grounded and computationally tractable ABN framework that allows agents to argue, negotiate, and resolve conflicts relating to their social influences within a multi-agent society. In particular, the model encapsulates four fundamental elements: (i) a scheme that captures the stereotypical pattern of reasoning about rights and obligations in an agent society, (ii) a mechanism to use this scheme to systematically identify social arguments to use in such contexts, (iii) a language and a protocol to govern the agent interactions, and (iv) a set of decision functions to enable agents to participate in such dialogues. Second, we use this framework to devise a series of concrete algorithms that give agents a set of ABN strategies to argue and resolve conflicts in a multi-agent task allocation scenario. In so doing, we exemplify the versatility of our framework and its ability to facilitate complex argumentation dialogues within artificial agent societies. Finally, we carry out a series of experiments to identify how and when argumentation can be useful for agent societies. In particular, our results show: a clear inverse correlation between the benefit of arguing and the resources available within the context; that when agents operate with imperfect knowledge, an arguing approach allows them to perform more effectively than a non-arguing one; that arguing earlier in an ABN interaction presents a more efficient method than arguing later in the interaction; and that allowing agents to negotiate their social influences presents both an effective and an efficient method that enhances their performance within a society.