We present an experimental study of decentralized two‐sided matching markets with no transfers. Experimental participants are informed of everyone's preferences and can make arbitrary nonbinding match offers that get finalized when a period of market inactivity has elapsed. Several insights emerge. First, stable outcomes are prevalent. Second, while centralized clearinghouses commonly aim at implementing extremal stable matchings, our decentralized markets most frequently culminate in the median stable matching. Third, preferences' cardinal representations impact the stable partners with whom participants match. Last, the dynamics underlying our results exhibit strategic sophistication, with agents successfully avoiding cycles of blocking pairs.