Individual versus social optimization in statistical estimation

A number of estimators participate in a non-cooperative game where the data they collect are reported to a central planner who takes decisions. She in her turn decides on the estimates to be imposed on the participants. Because they are aware of this, they may behave strategically and misreport. We exemplify this decision making process where the James-Stein's estimator is used by the central planner. In particular, we consider the resulting optimization or Nash equilibria reporting strategies in a number of variations of this game.