  We consider multi-player games played on graphs, in which the players aim at
fulfilling their own (not necessarily antagonistic) objectives. In the spirit
of evolutionary game theory, we suppose that the players have the right to
repeatedly update their respective strategies (for instance, to improve the
outcome w.r.t. the current strategy profile). This generates a dynamics in the
game which may eventually stabilise to an equilibrium. The objective of the
present paper is twofold. First, we aim at drawing a general framework to
reason about the termination of such dynamics. In particular, we identify
preorders on games (inspired from the classical notion of simulation between
transitions systems, and from the notion of graph minor) which preserve
termination of dynamics. Second, we show the applicability of the previously
developed framework to interdomain routing problems.
