Bipartite matching problem is to study two disjoint groups of agents who need to be matched pairwise. It can be applied to many real-world scenarios and explain many social phenomena. In this article, we study the effect of competition on bipartite matching problem by introducing correlated wish list. The results show that proper competition can improve the overall happiness of society and also reduce the instability of the matching result of unequal sized bipartite matching.
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