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. …

discrete interdependent risks with heterogeneous agents. There is a threat of an event that can only happen once, and the risk … depends on actions taken by others. Any agent's incentive to invest in managing the risk depends on the actions of others …. Security problems at airlines and in computer networks come into this category, as do problems of risk management in …