Repeated Network Games with Dominant Actions and Individual Rationality

Abstract

Three kinds of activities happen in a network: agents link or unlink, agents act, and agents observe and learn. The existing literature on network formation, on network games, and on monitoring 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 their neighbors. Agents learn by observing links, actions of their neighbors, and (perhaps) from a public signal. We dene 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 actions are strongly inter-dependent. When a dominant action is available to each agent and each agents individual rationality is satisfied, we prove a Convergence Theorem that characterizes the networks and actions that persist in the steady-state. We also show endogenously formed networks with the associated action proles often yield a higher social welfare than exogenously prescribed ones. Finally, we show that in the absence of an informative monitoring structure, cooperation in sparse networks may fail even when agents are patient.