Consider a simple dynamics ■廿matching f,廿blocking pair(m,w), o Remove the old pairing (m,f(m))and (w,f(w)) f(m):the woman matched to m in f.(f(w):similar.) Match m and w ▣Match f(m)andf(w) ■ Question:Would repeating this finally lead to a stable matching? W1>W2 mi m1>m2 W1>W2 m2 W2 m1>m2 14Consider a simple dynamics ◼ ∀ matching 𝑓, ∀ blocking pair (𝑚, 𝑤), ❑ Remove the old pairing 𝑚, 𝑓 𝑚 and 𝑤, 𝑓 𝑤 ◼ 𝑓(𝑚): the woman matched to 𝑚 in 𝑓. (𝑓(𝑤): similar.) ❑ Match 𝑚 and 𝑤 ❑ Match 𝑓 𝑚 and 𝑓(𝑤) ◼ Question: Would repeating this finally lead to a stable matching? 𝑚1 𝑤2 𝑤1 𝑚2 𝑤1 > 𝑤2 𝑤1 > 𝑤2 𝑚1 > 𝑚2 𝑚1 > 𝑚2 14