  Vertical federated learning (VFL) is a promising approach for collaboratively
training machine learning models using private data partitioned vertically
across different parties. Ideally in a VFL setting, the active party (party
possessing features of samples with labels) benefits by improving its machine
learning model through collaboration with some passive parties (parties
possessing additional features of the same samples without labels) in a privacy
preserving manner. However, motivating passive parties to participate in VFL
can be challenging. In this paper, we focus on the problem of allocating
incentives to the passive parties by the active party based on their
contributions to the VFL process. We formulate this problem as a variant of the
Nucleolus game theory concept, known as the Bankruptcy Problem, and solve it
using the Talmud's division rule. We evaluate our proposed method on synthetic
and real-world datasets and show that it ensures fairness and stability in
incentive allocation among passive parties who contribute their data to the
federated model. Additionally, we compare our method to the existing solution
of calculating Shapley values and show that our approach provides a more
efficient solution with fewer computations.
