Extensive-Form Argumentation Games.
Ariel D. Procaccia, Jeffrey S. Rosenschein · 2005
Two prevalent approaches to automated negotiation are the application of game-theoretic notions and the argumentation-based angle; these two schemes are frequently at odds. An elegant view of argumentation is Dung’s abstract argumentation theory [2], which cold-shoulders the internal structure of arguments in favor of the entire debate’s global structure. Dung’s theory is elaborated by work in dialectical argumentation theory, which focuses on dialogues between two players. In this paper, we enhance the abovementioned frameworks by considering two-agent settings where each of the agents is identified with a set of arguments. A binary attack relation between arguments is given, as well as (most importantly) a payoff function that assigns real values to every possible valid dialogue. Such game-based argumentation frameworks can be lucidly realized as games in extensive form (marrying, in a sense, the game-theoretic and argumentation-based approaches). We investigate specialized notions of “maximally-defendable ” sets of arguments, and the correlation between the properties of the agents ’ argument sets and the size of the associated game tree. Furthermore, algorithmic issues are considered: we present simplifications and efficient solutions for our argumentation games, and discuss a special case where the representation of the framework is logarithmic in the size of the associated game tree. 1