Connected Trading Cycles

2023-03-17

arXiv.org

AI Summary

In one-sided matching markets (e.g., housing markets), a fundamental tension exists between *invitation incentives* and *stability/optimality*, stemming from strategic competition between inviters and invitees—rendering classical notions incompatible with incentive compatibility. Method: We introduce a novel, relaxed definition of stability and optimality based on network connected components, formally characterizing the theoretical optimum achievable under strict incentive compatibility. Building upon this, we design the *Connected Trading Cycles* (CTC) mechanism—a graph-theoretic extension of the trading cycles framework that integrates game-theoretic reasoning, mechanism design, and connected-component analysis. Contribution: CTC is the first mechanism achieving both this newly defined optimality bound and strict incentive compatibility. Unlike prior mechanisms—which fail to jointly satisfy incentive compatibility, stability, and optimality—CTC attains the strongest feasible stability and optimality within each maximally connected subgraph. Our approach bridges matching theory, algorithmic game theory, and structural graph analysis.

Abstract

Incentivizing the existing participants to invite new participants to join an auction, matching or cooperative game have been extensively studied recently. One common challenge to design such incentive in these games is that the invitees and inviters are competitors. To have such an incentive, we normally have to sacrifice some of the traditional properties. Especially, in a housing market (one kind of one-sided matching), we cannot maintain the traditional stability and optimality. The previous studies proposed some new matching mechanisms to have the invitation incentive (part of the incentive compatibility), but did not have any guarantee on stability and optimality. In this paper, we propose new notions of stability and optimality which are achievable with incentive compatibility. We weaken stability and optimality on a special structure (complete components) on networks. We first prove that the weakened notions are the best we can achieve with incentive compatibility. Then, we propose three mechanisms (Swap With Neighbors, Leave and Share, and Connected Trading Cycles) to satisfy the desirable properties. Connected Trading Cycles is the first mechanism to satisfy the best stability and optimality compatible with incentive compatibility.

Problem

• Incentivize participants in auctions
• Balance invitation incentives with stability
• Develop mechanisms for optimal matching

Innovation

• Weakened stability and optimality
• Incentive compatibility in networks
• Connected Trading Cycles mechanism