Aggregate monotonic stable single‐valued solutions for cooperative games

This article considers single‐valued solutions of transferable utility cooperative games that satisfy core selection and aggregate monotonicity, defined either on the set of all games, G ^N , or on the set of essential games, E ^N (those with a non‐empty imputation set). The main result is that for an arbitrary set of players, core selection and aggregate monotonicity are compatible with individual rationality, the dummy player property and symmetry for single‐valued solutions defined on both G ^N and E ^N . This result solves an open question in the literature (see for example Young et al. Water Resour Res 18:463–475, 1982).