Lock-in through passive connections

We consider a model of social coordination and network formation where agents decide on an action in a coordination game and on whom to establish costly links to. We study the role of passive connections; these are connections to a given agent that are supported by other agents. Such passive connections may inhibit agents from switching actions and links, as this may result in a loss of payoff received through them. When agents are constrained in the number of links they may support, this endogenously arising form of lock-in leads to mixed profiles, where different agents choose different actions, being included in the set of Nash equilibria. Depending on the precise parameters of the model, risk- dominant, payoff- dominant, or mixed profiles are stochastically stable. Thus, agents’ welfare may be lower as compared to the case where payoff is only received through active links. The network formed by agents plays a crucial role for the propagation of actions, it allows for a contagious spread of risk dominant actions and evolves as agents change their links and actions.