Stable Marriage on Networks

Miao Li, Xinwei Song, Dengji Zhao

Keywords: Algorithmic game theory, Mechanism design, Two-sided matching, Social network

Abstract: We consider a stable marriage problem on a network, where two groups of agents (men and women) form the network and each only knows its neighbors. Our objective is to design a novel mechanism that motivates agents to invite their neighbors to participate in the matching game if they are not already in it and provides agents with more selections in the enlarged game. The difficulty is that invitees may make the inviters' allocation worse off, which occurs if we apply the classic Deferred Acceptance (DA) mechanism. To induce mutual invitations, one idea is to add restrictions on DA, allowing each agent to propose only to their neighbors, which ensures that everyone is eager to invite all their neighbors. The drawback is that agents can never match with non-neighbors. To combat this, we propose Dynamic Deferred Acceptance (DDA), which enables matching among non-neighbors through a closed alliance construction and a sharing process. We demonstrate several impossibility results regarding incentive compatibility, stability, and efficiency, and then construct the theoretical boundaries for our model. Finally, we prove that DDA is the first mechanism to achieve all these desirable properties.

Area: Game Theory and Economic Paradigms (GTEP)

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Submission Number: 1004