Multi-player and Multi-choice Quantum Game

We investigate a multi-player and multi-choice quantum game. We start from a two-player and two-choice game, and the result is better than its classical version. Then we extend this to N-player and N-choice cases. In the quantum domain, we provide a strategy with which players can always avoid the worst outcome. Also, by changing the value of the parameter of the initial state, the probabilities for players to obtain the best pay-off will be much higher that in its classical version.