Networks Emerging in a Volatile World

The paper proposes a model to study the conditions under which complex networks emerge (or not) when agents are involved in a dynamic coordination setup. The focus, however, is not on the classical issue of equilibrium selection - instead, our aim is to shed light on how agents' efforts to coordinate a¤ect the process of network formation in a large and complex environment. The model posits that, over time, new links are created if they are pro.table, and existing links disappear due to exogenous decay. Alongside this struggle between link creation and link destruction, agents' choices in the coordination game adapt to their current local conditions and thus coevolve with the social network. The dynamic behavior of the system is studied within di¤erent time scales (the long and ultralong runs), which di¤er in the role accorded to the noise that is induced by finite populations. We characterize analytically the evolution of the modelin each case and show that, depending on the time scale under consideration, the process displays discontinuous transitions in overall connectivity, resilient transformations in network topology, and equilibrium multiplicity. This behavior is akin to that observed concerning various network phenomena where coordination and network formation display mutually reinforcing roles.