There have been two main lines in the literature on restricted games: the f
irst line was started by Myerson (1977) that studied graph-restricted games
an the second one was initiated by Faigle (1989). The present paper provid
es a unified way to look on the literature and establishes connections betw
een the two different lines on restricted games. The strength and advantage
s of this unified approach becomes clear in the study of the inheritance of
the convexity from the game to the restricted game where an interesting re
sult by Nouweland and Borm (1991) on the convexity of graph-restricted game
s is turned into a direct consequence of the corresponding result by Faigle
(1989), by means of this relation.