Optimal Payoff Functions

The second paper finds an even better payoff function.
We define the aristocrat utility to be a measure between the players' actual action and its average action.
A player should use the AU as its payoff function to ensure good alignment between its payoffs and the global utility.
Unfortunately, doing so means that the player changes its average action, thereby obviating the derivation process. There are fixed-point solutions to this problem.
However, it is much easier to assume so fixed utility that does not depend on the player's, like WLU.
WLU can be modified to make it more like AU (less opaque) by clamping to a different set of actions.