A note on NTU convexity

For cooperative games with transferable utility, convexity has turned out to be an important and widely applicable concept. Convexity can be defined in a number of ways, each having its own specific attractions. Basically, these definitions fall into two categories, namely those based on a supermodular interpretation and those based on a marginalistic interpretation. For games with nontransferable utility, however, the literature mainly focuses on two kinds of convexity, ordinal and cardinal convexity, which both extend the supermodular interpretation. In this paper, we analyse three types of convexity for NTU games that generalise the marginalistic interpretation of convexity.