Persuading Stable Matching

In bipartite matching problems, agents on two sides of a graph want to be paired according to their preferences. The stability of a matching depends on these preferences, which in uncertain environments also reflect agents' beliefs about the underlying state of the world. We investigate how a principal -- who observes the true state of the world -- can strategically shape these beliefs through Bayesian persuasion to induce stable matching that maximizes a desired utility. Due to the general intractability of the underlying matching optimization problem as well as the multi-receiver persuasion problem, our main considerations are two important special cases: (1) when agents can be categorized into a small number of types based on their value functions, and (2) when the number of possible world states is small. For each case, we study both public and private signaling settings. Our results draw a complete complexity landscape: we show that private persuasion remains intractable even when the number of worlds is small, while all other settings admit polynomial-time algorithms. We present efficient algorithms for each tractable case and prove NP-hardness for the intractable ones. These results illuminate the algorithmic frontier of stable matching under information design and clarify when optimal persuasion is computationally feasible.