Information aggregation in a beauty contest game

We consider a repeated game in which a team of agents share a common, but only partially known, task. The team also has the goal to coordinate while completing the task. This creates a trade-off between estimating the task and coordinating with others reminiscent of the kind of trade-off exemplified by the Keynesian beauty contest game. The agents thus can benefit from learning from others. This paper provides a survey of results from [1-4]. We first present a recent result that states repeated play of the game by myopic but Bayesian agents, who observe the actions of their neighbors over a connected network, eventually yield coordination on a single action. Furthermore, the coordinated action is equal to the mean estimate of the common task given individual's information. This indicates that agents in the network have the same mean estimate in the limit despite the differences in the quality of local information. Finally, we state that if the space of signals is a finite set, the coordinated action is equal to the estimate of the common task given full information, that is, agents eventually aggregate the information available throughout the network on the common task optimally.