科研之友
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摘要
Gale and Shapley (1962) have shown that in marriage markets, where men and women have preferences over potential partners of the other gender, a stable matching always exists. In this paper, we study a more general framework with d different genders due to Knuth (1976). The genders are ordered in a directed cycle and agents only have preferences over agents of the subsequent gender. Agents are then matched into families, which contain exactly one agent of each gender. We show that there, always exists a stable matching if there are at most d+1 agents per gender, thereby generalizing and extending previous results. The proof is constructive and computationally efficient.
- 出版日期2016-7
