Abstract
We define a generic notion of abstract games of argumentation strategy for (attack-only and bipolar) argumentation frameworks, which are zero-sum games whereby two players put forward sets of arguments and get a reward for their combined choices. The value of these games, in the classical game-theoretic sense, can be used to define measures of (quantitative) game-theoretic strength of arguments, which are different depending on whether either or both players have an “agenda” (i.e. an argument they want to be accepted). We show that this general scheme captures as a special instance a previous proposal in the literature (single agenda, attack-only frameworks), and seamlessly supports the definition of a spectrum of novel measures of game-theoretic strength where both players have an agenda and/or bipolar frameworks are considered. We then discuss the applicability of these instances of game-theoretic strength in different contexts and analyse their basic properties.
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Here \({\mathcal P}^T\) is the transpose of vector \({\mathcal P}\).
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Note that we resort here to an intuitive interpretation of the notions of attack and support, based on human understanding of the natural language description of the arguments. In other words, these relations are produced by manual annotation and we acknowledge that the relevant interpretation may not be univocal. Possible differences in this respect do not affect the main points of our discussion here anyway.
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Even the requirement of conflict-freeness seems to be overlooked in some cases.
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Baroni, P., Comini, G., Rago, A., Toni, F. (2017). Abstract Games of Argumentation Strategy and Game-Theoretical Argument Strength. In: An, B., Bazzan, A., Leite, J., Villata, S., van der Torre, L. (eds) PRIMA 2017: Principles and Practice of Multi-Agent Systems. PRIMA 2017. Lecture Notes in Computer Science(), vol 10621. Springer, Cham. https://doi.org/10.1007/978-3-319-69131-2_24
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