  It is well known that a non-cooperative game may have multiple equilibria. In
this paper we consider the efficiency of games, measured by the ratio between
the aggregate payoff over all Nash equilibria and that over all admissible
controls. Such efficiency operator is typically unstable with respect to small
perturbation of the game. This seemingly bad property can actually be a good
news in practice: it is possible that a small change of the game mechanism may
improve the efficiency of the game dramatically. We shall introduce a game
mediator with limited resources and investigate the mechanism designs aiming to
improve the efficiency.
