The reduction of qualitative games

Abstract: We extend the study of the iterated elimination of strictly dominated strategies (IESDS) from Nash strategic games to a class of qualitative games. Also in this case, the IESDS process leads us to a kind of 'rationalizable' result. We define several types of dominance relation and game reduction and establish conditions under which a unique and nonempty maximal reduction exists. We generalize, in this way, some results due to Dufwenberg and Stegeman (2002) and Apt (2007).