WEBVTT

cue-001
00:00:00.790 --> 00:00:03.205
A stable match should keep its certificate.

cue-002
00:00:06.100 --> 00:00:09.420
Bob prefers x, so Bob gets x and

cue-003
00:00:09.420 --> 00:00:11.162
Alice gets y.

cue-004
00:00:12.940 --> 00:00:16.237
Exact, stable, proposer-optimal, and

cue-005
00:00:16.237 --> 00:00:17.305
complete.

cue-006
00:00:18.740 --> 00:00:21.747
Now switch one ordinary input. Bob

cue-007
00:00:21.747 --> 00:00:22.873
prefers y.

cue-008
00:00:26.740 --> 00:00:30.211
The matching reorganizes. Alice gets x,

cue-009
00:00:30.211 --> 00:00:31.941
and Bob gets y.

cue-010
00:00:34.060 --> 00:00:37.206
Again the result is exact and certified, with

cue-011
00:00:37.206 --> 00:00:39.122
nobody left unmatched.

cue-012
00:00:44.050 --> 00:00:46.326
New preference. Same proof.