  Three player quantum Kolkata restaurant problem is modeled using three
entangled qutrits. This first use of three level quantum states in this context
is a step towards a $N$-choice generalization of the $N$-player quantum
minority game. It is shown that a better than classical payoff is achieved by a
Nash equilibrium solution where the space of available strategies is spanned by
subsets of SU(3) and the players share a tripartite entangled initial state.
