A modified deferred acceptance algorithm for many-to-one matching markets with externalities among firms

Two-Sided Matching With Externalities: A Survey

“…Moreover, under the same assumption, Bando [7] shows that worker-optimal and worker-worst quasi stable matchings exist. We will introduce the main result of Bando [7] in the next section.…”

“…7 Therefore, s / ∈ Ch c (T 1 c ) must also hold. In the 7 The first equality is a direct consequence of a property of choice sets called consistency, while the second equality uses idempotence. See, for example, Alkan [3].…”

“…In fact, we can directly apply the approach of Sasaki and Toda [61,62] into this model. Bando [6,7] takes a different approach from Sasaki and Toda [61,62]. As we saw in Section 1.3, the choice function is a useful tool to analyze a classical model.…”

“…As we saw in Section 1.3, the choice function is a useful tool to analyze a classical model. Bando [6,7] extends the choice function approach into the market with externalities. We summarize the results of Bando [6,7].…”

“…However, it is not worker-optimal because ({w 2 }, {w 3 }, {w 1 }) is also a quasi stable matching □ In the above example, the sequential DA algorithm finds a quasi stable matching. However, in general, Bando [7] shows that the sequential DA algorithm may not find even a quasi stable matching. The reason for the failure of the algorithm is that each firm chooses its workers based on the current matching.…”