Bankruptcy and the per capita nucleolus: The claim-and-right rules family

• A new bankruptcy rule; the clights rule.
• It is shown that the clights rule corresponds to the per capita nucleolus.
• Properties of the clights rule are analyzed.
• The unifying class of claim-and-right rules.
• A new type of Kohlberg criterion for the (per capita) nucleolus.

This article describes the per capita nucleolus for bankruptcy games as a bankruptcy rule. This rule, called the clights rule, is based on the well-known constrained equal awards principle and it takes into account a vector of clights, a new term which is a blend of claims and rights. These clights only depend on the vector of claims while the height of the estate determines whether the clights should be interpreted as modified claims or as rights. It is shown that both the clights rule and the Aumann–Maschler rule can be captured within the family of so-called claim-and-right rules.