Matching with Budget Constraints

We study a matching model with salaries in which firms face budget constraints. Due to budget constraints, the existence of a stable matching is not guaranteed. We show that if workers are homogeneous, from the firms' point of view, then a weak stable matching always exists; furthermore, when a strong stable matching does not exist, there is a nearby budget vector for firms such that a strong stable matching exists for the problem with perturbed budgets. On the flip side, if firms are homogeneous from the workers' point of view, a stable matching may not exist; however, one can reach a stable matching by changing the budget of firms where the total budget remains the same and each firm's budget change is bounded by the value of at most one worker to that firm