The game of n-player Cutcake

The game of n-player Cutcake is the n-player version of Cutcake, a classical combinatorial game. Even though determining the solution of Cutcake is trivial, solving the n-player variant is challenging because of the identification of queer games, i.e., games where no player has a winning strategy. A classification of the instances of n-player Cutcake is presented.