  We want to introduce another smoothing approach by treating each geometric
element as a player in a game: a quest for the best element quality. In other
words, each player has the goal of becoming as regular as possible. The set of
strategies for each element is given by all translations of its vertices.
Ideally, he would like to quantify this regularity using a quality measure
which corresponds to the utility function in game theory. Each player is aware
of the other players' utility functions as well as their set of strategies,
which is analogous to his own utility function and strategies. In the simplest
case, the utility functions only depend on the regularity. In more complicated
cases this utility function depends on the element size, the curvature, or even
the solution to a differential equation. This article is a sketch of a possible
game-theoretical approach to mesh smoothing and still on-going research.
