The paper studies the class SC(N) of cooperative games with player set N which have the semiconvexity property. SC(N) is decomposed into an algebraic sum of convex cones of games for which generating sets are available. The union of these sets thus forms a generating set for SC(N). Special attention is paid to one of the considered cones in the decomposition of SC(N). In particular, the so called airport savings games w(y), y is-an-element-of R(N) defined by w(y)(S) = SIGMA(j is-an-element-of S)y(j) - max(j is-an-element-of S)y(j) for 0 not-equal S subset-or-equal-to N, are emphasized.