The name of a game from the 2013 Putnam

Does the following game from the 2013 Putnam have an official name? Based on my searches, it seems to have been created just for the exam.

Let $n\geq 1$ be an odd integer. Alice and Bob play the following game, taking alternating turns, with Alice playing first. The playing area consists of $n$ spaces, arranged in a line. Initially all spaces are empty. At each turn, a player either

• places a stone in an empty space, or

• removes a stone from a nonempty space $s$, places a stone in the nearest empty space to the left of s (if such a space exists), and places a stone in the nearest empty space to the right of s (if such a space exists).

Furthermore, a move is permitted only if the resulting position has not occurred previously in the game. A player loses if he or she is unable to move. Assuming that both players play optimally throughout the game, what moves may Alice make on her first turn?

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