theory and analyze the Shapley value to resolve such liability problems. We establish three main monotonicity properties of …In a liability problem, the asset value of an insolvent firm must be distributed among the creditors and the firm … increase of the asset value. Even though liability games are constant-sum games and we show that the Shapley value can be …

the firm among the creditors and the firm itself. Compared to standard bankruptcy games as studied in the game theory … literature, we introduce the firm as an explicit player and define a new class of transferable utility games called liability … games. Liability games are superadditive, constant sum, partially convex, and partially concave. The core of a liability …

performing agent must beat the second best to receive the winner prize. We analyze a tournament with two risk averse agents …. Under unlimited liability, the principal strictly benefits from a gap by partially insuring the agents and thereby reducing … labor costs. If the agents are protected by limited liability, the principal sticks to the standard tournament. …