One-Sided Matching with Permission

Classic one-sided matching assumes participants are independent and known in advance, each with an initial endowment to exchange with others. In this paper, we consider the participants are connected to form a network, which is often the case in reality. Some participants from the network initiate the matching game and the others need the existing participants' invitation/permission to join the game. The challenge is that participants may compete with each other if we apply the classic solution Top Trading Cycle (TTC), so they would not invite each other. Although we can add constraints on TTC to incentivize participants to invite each other, it only works on very limited networks. To combat this, we propose a new matching mechanism called Leave and Share to work on all networks. We prove that our solution is the most stable matching in all networks. In terms of optimality, as it is impossible to achieve it in any network, we conduct simulations to compare it with the extensions of TTC.