  We introduce differential games for FO logic of graphs, a variant of
Ehrenfeucht-Fra\"{i}ss\'e games in which the game is played on only one graph
and the moves of both players restricted. We prove that, in a certain sense,
these games are strong enough to capture essential information about graphs
from graph classes which are interpretable in nowhere dense graph classes.
This, together with the newly introduced notion of differential locality and
the fact that the restriction of possible moves by the players makes it easy to
decide the winner of the game in some cases, leads to a new approach to the FO
model checking problem on interpretations of nowhere dense graph classes.

Logic in Computer Science;Discrete Mathematics;Combinatorics