Level-structure value versus recursive bargaining payoffs

Determine whether the payoff map generated by the hierarchical weighted-Nash sharing rule coincides with the level-structure value of Winter, or merely resembles it.

Background

The model represents agreements as laminar hierarchies, which correspond to level structures in cooperative game theory. Under fixed weighted-Nash shares, payoffs are generated recursively by bargaining at each agreement level against the state in which that agreement is absent.

The paper notes that this construction and Winter's level-structure value use related ingredients but different recursions. Establishing equivalence, or proving that they differ and characterizing the difference, would clarify the cooperative-game interpretation of the sharing rule.

References

Whether the resulting map from states to payoff vectors coincides with the level-structure value of \citet{Winter1989}, or merely resembles it, we have not determined; the two are built from the same ingredients but not by the same recursion, and settling it would be a worthwhile exercise.

— Does the grand coalition form? Persistence, arrival, and the role of the sharing rule in a dynamic process of nested binding agreements  (2608.17766 - Heitzig, 18 Aug 2026) in Section (A cooperative-game reading)