Abstract
In this paper, we analyze bankruptcy problems with nontransferable utility (NTU) from a game theoretical perspective by redefining corresponding NTU-bankruptcy games in a tailor-made way. It is shown that NTU-bankruptcy games are both coalition-merge convex and ordinally convex. Generalizing the notions of core cover and compromise stability for transferable utility (TU) games to NTU-games, we also show that each NTU-bankruptcy game is compromise stable. Thus, NTU-bankruptcy games are shown to retain the two characterizing properties of TU-bankruptcy games: convexity and compromise stability. As a first example of a game theoretical NTU-bankruptcy rule, we analyze the adjusted proportional rule and show that this rule corresponds to the compromise value of NTU-bankruptcy games.
Highlights
In a (TU-)bankruptcy problem there is a group of agents with legal monetary claims over an estate, which is not large enough to satisfy the total claim
We investigate bankruptcy problems with nontransferable utility, in short NTU-bankruptcy problems, which are a generalization of bankruptcy problems
Orshan et al (2003) are the first to analyze NTUbankruptcy problems in a game theoretical framework. They associate an NTU-game to an NTU-bankruptcy problem and show that the intersection of the core and the bilateral consistent prekernel of such a game is nonempty
Summary
In a (TU-)bankruptcy problem there is a group of agents with legal monetary claims over an estate, which is not large enough to satisfy the total claim. They associate an NTU-game to an NTU-bankruptcy problem and show that the intersection of the core and the bilateral consistent prekernel of such a game is nonempty They provide an example which illustrates that their game need not be superadditive and, not ordinally convex. The reason for this is twofold: first, the value of a coalition may contain payoff vectors assigning a level of utility to a member of the coalition which exceeds his claim; second, the value of a coalition may contain elements that are not in the comprehensive hull of the set E. Dietzenbacher (2018) has analyzed NTU-bankruptcy problems using a different NTU-modeling approach, showing that the core of this alternative game coincides with the core cover and the reasonable set.
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