Game-Theoretic Foundations for Argumentation

Game theory is becoming central to the design and analysis of computational mechanisms in which multiple entities interact strategically. In particular, the tools of mechanism design are used extensively to engineer incentives for truth-revelation into resource-allocation and preferenceaggregation protocols, as evident in the work on combinatorial auctions and voting. On the other hand, traditionally, the design of logical reasoning procedures assumes that all logical formulae are available a priori for reasoning by a single agent. However, for reasoning using knowledge obtained from different entities in an open system (e.g. the Semantic Web), incentives are clearly equally important. Just as an auction is a rule that maps the bids of different agents into a social outcome by allocating resources, an inference procedure can map logical formulae revealed by different agents into logical conclusions. It is somewhat surprising that, to date, very little systematic investigation of incentives has been applied in the context of logical inference when formulae are distributed among self-interested agents. Against this background, we ask: how do we engineer inference procedures with desirable incentive properties, when knowledge is distributed among strategic agents? A general answer to this question requires a new paradigm, and is beyond a single paper. Our aim is to motivate such paradigm by exploring the question in the context of Dung’s abstract argumentation theory, which generalises a variety of nonmonotonic logics. We introduce Argumentation Mechanism Design (ArgMD), in which argument evaluation procedures are viewed as games with different agents deciding which arguments to reveal. We then undertake a detailed case study of the strategic properties of grounded semantics under different conditions. We close by making general remarks about how this framework may be further generalised.