On a super large fixed-point of common information in multi-agent signalling games
Anton Benz · Logic Journal of IGPL · 2011
In this article, we compare two fixed-point constructions of common knowledge in sequential coordination problems. The first one corresponds to the standard maximal fixed-point construction of common knowledge in a possible worlds framework; the second construction provides an even larger fixed-point and involves iterated epistemic updates. We call the first fixed-point the maximal fixed-point, and the second the update fixed-point. Both fixed-points define a set of sequential actions that solve the coordination problem such that success is mutually guaranteed. The main application intended is the study of signalling games as introduced by [15]. We introduce a non-probabilistic version of these games as multi-agent signalling games. We use them for modelling prototypical accommodation phenomena following [16]. We show especially that accommodation, which involves presupposition violation, is only licensed due to the existence of the super large update fixed-point, whereas the literal language use without presupposition violations can be characterized by the maximal fixed-point.