Stable outcomes of the roommate game with transferable utility

We consider the transferable utility (TU) version of Gale and Shapley's roommate game. We find several results that are analogous to known results for the non-transferable utility game, such as a characterization of stable outcomes by forbidden minors, a characterization of the extreme points of the core, and a median property of stable outcomes. The TU roommate game is a special case of the TU partitioning game of Kaneko and Wooders. Bondareva and Shapley's balancedness condition for the core of such games is the starting point for our forbidden minors approach.