Optimism leads to optimality: Ambiguity in network formation

Abstract

We analyze a model of endogenous two-sided network formation where players are affected by uncertainty about their opponents' decisions. We model this uncertainty using the notion of equilibrium under ambiguity as in Eichberger and Kelsey (2014). Unlike the set of Nash equilibria, the set of equilibria under ambiguity does not always include underconnected and thus inefficient networks such as the empty network. On the other hand, it may include networks with unreciprocated, one-way links, which comes with an efficiency loss as linking efforts are costly. We characterize equilibria under ambiguity and provide conditions under which increased player optimism comes with an increase in connectivity and realized benefits in equilibrium. Next, we analyze network realignment under a myopic updating process with optimistic shocks and derive a global stability condition of efficient networks in the sense of Kandori et al. (1993). Under this condition, a subset of the Pareto optimal equilibrium networks is reached, specifically, networks that maximize the players' total benefits of connections.