Applications of the Shapley Value to Financial Problems

Managing risk, matching resources efficiently, and ensuring fair allocation are fundamental challenges in both finance and decision-making processes. In many scenarios, participants contribute unequally to collective outcomes, raising the question of how to distribute costs, benefits, or opportunities in a justifiable and optimal manner. This paper applies the Shapley value—a solution concept from cooperative game theory—as a principled tool in the following two specific financial settings: first, in tax cooperation games; and second, in assignment markets. In tax cooperation games, we use the Shapley value to determine the equitable tax burden distribution among three firms, A, B, and C, which operate in two countries, Italy and Poland. Our model ensures that countries participating in coalitions face a lower degree of tax evasion compared to non-members, and that cooperating firms benefit from discounted tax liabilities. This structure incentivizes coalition formation and reveals the economic advantage of joint participation. In assignment markets, we use the Shapley value to find the optimal pairing in a four-buyers and four-sellers housing market. Our findings show that the Shapley value provides a rigorous framework for capturing the relative importance of participants in the coalition, leading to more balanced tax allocations and fairer market transactions. Our theoretical insights with computational techniques highlights the Shapley value’s effectiveness in addressing complex allocation challenges across financial management domains.