Philosophical dialogue games have been used widely as models for protocols in multi-agent systems to improve flexibility, expressiveness, robustness and efficiency. However, many dialogue games are effectively based on propositional logic, which is not always sufficiently expressive for artificial reasoning. In particular they do not allow for a strong connection between computational models of dialogic argument and mature mathematical models of abstract argument structures, which support a range of sophisticated agent reasoning systems. In this paper we describe how an existing dialogue game - Walton & Krabbe's RPD_0 - may be adapted by using Dung Argumentation Frameworks in place of propositional logic. We call this new dialogue game RPD_(GD), and describe some of its advantages over RPD_0, chiefly (i) that it allows the proponent to win by exploiting not just defects in the opponent's reasoning or inconsistency in its knowledge base, but also the incompleteness of its knowledge (ii) that it thus provides wider scope for strategic sophistication in multi-agent dialogue. We make two linked observations relating to strategy in RPDGD dialogues - first, that there are minimal sets of beliefs that one agent must hold, in order to know (assuming the correctness of those beliefs) whether it can successfully persuade another; and second, that the would-be persuader may regulate its utterances, in order to avoid acquiring at least some of the information which is outside these minimal amounts and thus irrelevant. We consider these observations using the concepts Minimum Sufficient Contextual Knowledge (MSCK) and fortification respectively. We demonstrate that in even very simple situations a strategy informed by these concepts can mean the difference between winning and losing a given encounter.
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