turkmath.org

The content of this talk is two papers of mine. Two different problems in cooperative game theory, which are related indirectly, are studied. First, I will give some basic notions related to cooperative game theory. In the first paper, different notions of merge proofness for allocation rules pertaining to transferable utility games are introduced. Relations between these merge proofness notions are studied, and some impossibility as well as possibility results for allocation rules are established. In the second paper, a decomposition of transferable utility games is introduced. Using the decomposition and the notion of minimal balanced collections, a set of necessary and sufficient conditions for a transferable utility game to have a singleton core is given. I will talk about both of the problems and give the relation between the two problems. The level of the talk is suitable for any listener who knows basic mathematics.