Repeated Network Games

Abstract

Three kinds of activities happen in a network: agents link or unlink; agents act; agents observe and learn. The existing literature on network formation, on network games and on monitoring and learning in networks studies each of these in isolation. We propose a framework in which these happen together. In our model, agents repeatedly choose to whom they link and the actions they take with those to whom they are linked. Agents learn by observing links, actions of those to whom they are linked and (perhaps) from a public signal. We define a repeated network game and an equilibrium of this game. An essential feature is that the network formed and hence the games played are determined endogenously and may be different at each moment of time. Equilibrium networks and equilibrium actions are strongly inter-dependent. Under assumptions we prove a Network Folk Theorem that (almost) characterizes the networks and action pro files that can be sustained in the steady-state of the network formation game. We also show endogenously formed networks with the associated action pro les often yield a higher social welfare than exogenously prescribed ones. We also highlight the importance of having an informative monitoring structure, and show that in its absence cooperation in sparse networks may fail even when agents are very patient.