Dynamic games with side information in economic networks

We consider a dynamic game with payoff externalities. Agents´ utility depends on an unknown true state of the world and actions of everyone in the network. Each agent has an initial private information about the underlying state and repeatedly observes actions of its neighbors. We analyze the asymptotic behavior of agents´ actions and beliefs in a connected network when it is common knowledge that the agents are myopic and rational. Given a quadratic payoff function, we provide a new proof for an existing result that claims almost sure consensus in actions asymptotically. Given consensus in actions, we show that agents have the same mean estimate of the true state of the world in the limit. We justify these results in a numerical example motivated by a socio-economic scenario.