Circular Networks as Efficient Nash Equilibria: Two Approaches

The present paper analyzes a network formation problem, and in particular the existence of circular networks that constitute efficient Nash equilibria. We consider two ways in which they may arise as solutions. One in the framework presented by Bala and Goyal. In it an agent receives a payoff which is increasing in the number of agents to which he is directly or indirectly connected, while it is decreasing in the number of agents to whom he is directly connected. The other approach departs from their assumptions in two crucial aspects. On one hand, we assume that connecting to an agent pays off not only for the number of connections that the agent can provide but also for her intrinsic value. On the other hand, we assume that each path connecting two agents has an associated cost which is the sum of the number of edges it includes, and which has to be paid by each agent in the path. In both approaches it is possible to obtain circular networks as efficient Nash equilibria. But, while in Bala and Goyal’s approach this is only one possibility (the other is the empty network), in our alternative approach, if the number of agents is larger than 3, it is the unique result.