Decentralized job matching

This paper studies a multi-stage decentralized matching model where firms sequentially propose their (unique) positions to workers. At each stage workers sequentially decide which offer to accept (if any). A firm whose offer has been declined may make an offer to another worker in the next stage. The game stops when all firms either have been matched to a worker or have already made unsuccessful offers to any worker remaining in the market. We show that there is a unique subgame-perfect equilibrium outcome, the worker-optimal matching. Firms in this game have a weakly dominant strategy, which consists of making offers in the same order as given by their preferences. When workers play simultaneously any stable matching can be obtained as an equilibrium outcome, but an unstable matching can obtain in equilibrium.