A Belief-based Approach to Network Formation

In this paper we consider four different game-theoretic approaches to describe the formation of social networks under mutual consent and costly communication. First, we consider Jackson-Wolinsky�s concept of pairwise stability. Next, we introduce a stronger version of this concept based on linking decisions by nodes, denoted as strict pairwise stability. Third, we consider Myerson�s consent game and its Nash equilibria. Fourth, within the context of Myerson�s consent game, we consider self-confirming equilibria based on simple myopic belief systems. We provide an exhaustive comparison of the classes of equilibrium networks that result from each of these four approaches. We determine the conditions under which there is equivalence of pairwise stability and strict pairwise stability. Second, we show that the Nash equilibria of Myerson�s consent game form a super set of the class of pairwise stable networks, while strict pairwise stability and monadic stability are fully equivalent.