An Incomplete Cooperation Structure for a Voting Game Can Be Strategically Stable

Abstract Aumann and Myerson (1988) defined a noncooperative linking game leading to the formation of cooperation structures. They asked whether it is possible for a simple game to have a stable structure in which no coalition forms, i.e., in which the cooperation graph is not internally complete but is connected and stable. We answer this question affirmatively; specifically, we present a simple proper weighted majority game with a connected incomplete structure, and we prove it to be stable under any protocol for the strategic formation of new links. This result implies that strategically refused communication can be a robust stable phenomena. Journal of Economic Literature Classification Numbers: C71, C72.