Stable Matching

Stable matching addresses the problem of optimally pairing agents from two sets based on their preferences, aiming to find a stable solution where no two agents would prefer each other to their assigned partners. Current research focuses on extending existing algorithms like Gale-Shapley to handle incomplete or tied preferences, incorporating learning mechanisms to address unknown preferences, and developing efficient algorithms for large-scale problems, including those involving couples or teams. These advancements are crucial for improving the fairness and efficiency of real-world applications such as resource allocation, job markets, and ride-sharing platforms, while also advancing our understanding of game-theoretic equilibria in decentralized systems.