  We investigate a multi-player and multi-choice quantum game. We start from
two-player and two-choice game and the result is better than its classical
version. Then we extend it 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 payoff will be much higher that in
its classical version.
