Matching workers to firms facing budget constraints

We study a many-to-one matching model with salaries in which firms face budget constraints. Mongell and Roth (1986) show that when firms face a budget constraint, a stable matching may not exist. We introduce an algorithm to find a strong stable matching by changing the budget of firms such that the total budget remains the same and each firm’s budget change is bounded by the value of at most one worker for that firm. • A many-to-one matching with salaries in which firms face budget constraints. • Mongell and Roth (1986) show that a stable matching may not exist. • Introduce an algorithm to find a strong stable matching by changing the budgets. • Each firm’s budget change is bounded by the value of at most one worker. • Moreover, the total budget of all firms remains the same.