Stable and Efficient Networks with Farsighted Players: the Largest Consistent Set

In this paper we study strategic formation of bilateral networks with farsighted players in the classic framework of Jackson and Wolinsky (1996). We use the largest consistent set (LCS)(Chwe (1994)) as the solution concept for stability. We show that there exists a value function such that for every component balanced and anonymous allocation rule, the corresponding LCS does not contain any strongly efficient network. Using Pareto efficiency, a weaker concept of efficiency, we get a more positive result. However, then also, at least one environment of networks (with a component balanced and anonymous allocation rule) exists for which the largest consistent set does not contain any Pareto efficient network. These confirm that the well-known problem of the incompatibility between the set of stable networks and the set of efficient networks persists even in the environment with farsighted players. Next we study some possibilities of resolving this incompatibility.