On the concavity of delivery games

Delivery games, introduced by Hamers, Borm, van de Leensel and Tijs in 1994, are combinatorial optimization games that arise from delivery problems closely related to the Chinese postman problem. They showed that delivery games are not necessarily balanced. For delivery problems 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 not be concave. The main result will be that for delivery problems corresponding to the class of bridge-connected cyclic graphs, which is a subclass of the class of bridge-connected Euler graphs, the related delivery games are concave. Further, we discuss some extreme points of the core and the τ-value for this class of concave delivery games.