Applying Abstract Argumentation Theory to Cooperative Game Theory

TL;DR

This paper explores the connection between abstract argumentation theory and cooperative game theory, showing how certain argumentation semantics correspond to solution concepts and analyzing their applicability to convex games.

Contribution

It extends Dung's argumentation semantics to cooperative game solutions and investigates the relationship with convex games, including limitations for three-player cases.

Findings

Complete extensions correspond to Roth's subsolutions and supercore.

Well-founded frameworks coincide with convex game solutions.

Three-player convex games lack well-founded argumentation frameworks.

Abstract

We apply ideas from abstract argumentation theory to study cooperative game theory. Building on Dung's results in his seminal paper, we further the correspondence between Dung's four argumentation semantics and solution concepts in cooperative game theory by showing that complete extensions (the grounded extension) correspond to Roth's subsolutions (respectively, the supercore). We then investigate the relationship between well-founded argumentation frameworks and convex games, where in each case the semantics (respectively, solution concepts) coincide; we prove that three-player convex games do not in general have well-founded argumentation frameworks.