Delivery games, introduced by Hamers, Borm, van de Leensel and Tijs in
1994, are combinatorial optimization games that arise from delivery p
roblems closely related to the Chinese postman problem (CPP). They sho
wed that delivery games are not necessarily balanced. For delivery pro
blems corresponding to the class of bridge-connected Euler graphs they
showed that the related games are balanced. This paper focuses on the
concavity property for delivery games. A delivery game arising from a
delivery model corresponding to a bridge-connected Euler graph need n
ot be concave. The main result will be that for delivery problems corr
esponding to the class of bridge-connected cyclic graphs, which is a s
ubclass of the class of bridge-connected Euler graphs, the related del
ivery games are concave, Further, we discuss some extreme points of th
e core and the tau-value for this class of concave delivery games. (C)
1997 Elsevier Science B.V.