This is a basic joseki, this shape is also extremely common with pincer and double approach joseki.
In 99% of situations, hane and connect should be the correct response.
Black 1 retreat, allowing white to get the corner, usually is not a good choice.
White 2 may also emphasize on the edge to prevent the cut, black 3 may not be a sente.
Afterall, if white is concern about the cut, white 2 could connect, black 3 is still a very great move.
Otherwise, white could get to play point A, which is the base for both sides. It is difficult for black to defend the defect of B efficiently. So, normally, hane and connect is just better than the retreat.
But there are always exceptions! The value to block the edge is not great in this situation, Q11 retreat is better than R11 hane.
After white retreat, if black connect, it is more valuable for white to expend the centre rather than bending at R11.
If black 2 extend into the edge, white 3 cut would be a severe move.
This game is Ke Jie 9p (Black) versus Ding Hao 9p, a game from the Chinese League. At this moment, AI think both A and B are very close in terms of value, but AI also prefer retreat at A more.
In the real game, Ding Hao played hane to get the corner, but black advanced on the edge, it is more satisfying for black.
White 1 and 3 seems to be a better direction to play.
This game is more unique, it is the game between Nakamura Sumire (White) and Oh-Yujin, guess the next move!
Nakamura played the blue point (AI suggestion!), giving up the points at the corner but attacking the two black stones directly, very aggressive! She won the game with excellent performance.
Very interesting.