On solving mutual liability problems

Area of Science:

• Game Theory
• Mathematical Economics
• Fair Division

Background:

• Bankruptcy problems involve distributing assets among creditors.
• Mutual liability problems generalize this by including inter-agent claims and debts.

Purpose of the Study:

• To introduce and analyze mutual liability problems as a generalization of bankruptcy problems.
• To define and characterize mutual liability rules based on bilateral transfer schemes.
• To extend axiomatic characterizations to mutual liability contexts.

Main Methods:

• Analysis of bilateral transfer schemes based on bankruptcy rules.
• Development of a unique transfer allocation for mutual liability problems.
• Axiomatic characterization for hierarchical mutual liability problems.

Main Results:

• Demonstration that bilateral transfer schemes lead to a unique allocation in mutual liability problems.
• Definition of unique mutual liability rules derived from bankruptcy rules.
• Extension of the Talmud rule's axiomatic characterization to mutual liability.

Conclusions:

• Mutual liability problems offer a broader framework for resource allocation with interdependencies.
• The proposed rules ensure a unique and equitable distribution of available cash.
• Axiomatic approaches provide robust methods for characterizing fair allocation rules in complex scenarios.