Who Ends Up with Z

Four men (a, b, c, d) and four women (W, X, Y, Z) have strict preference lists, most preferred first: - a: W, X, Y, Z - b: X, W, Z, Y - c: W, X, Z, Y - d: Y, Z, W, X - W: c, b, d, a - X: a, b, c, d - Y: b, c, a, d - Z: d, c, a, b Run the Gale-Shapley algorithm with the men proposing: each unmatched man proposes to the best woman who has not yet rejected him, and each woman keeps the best proposer so far, rejecting the rest. Which man is matched to Z when the algorithm stops? Answer with the man's letter.

• optimal stopping

Source: Gale-Shapley deferred acceptance (Gale and Shapley, 1962); the preference lists are invented for AxiomIQ. Statement written for AxiomIQ.