Promoting coordination in summary-statistic games

This paper studies how external incentives can help agents to coordinate in summary-statistic games. Agents follow a myopic best-reply rule and face a trade-off between efficiency and strategic uncertainty. A principal can help agents to coordinate on the Pareto optimal equilibrium by monitoring an appropriate number of agents. The optimal monitoring policy is 'minimally-invasive' - for every strategy profile of the agents, the principal either monitors just enough agents to make high effort a best-reply or does not monitor at all. Furthermore, given the principal's payoffs are supermodular and increasing at an increasing rate, the optimal monitoring policy is monotone in the number of agents who choose high effort.