Three player quantum Kolkata restaurant problem is modelled 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.
The Quantum Kolkata restaurant problem is a multiple-choice version of the quantum minority game, where a set of n non-communicating players have to chose between one of m choices. A payoff is granted to the players that make a unique choice. It has previously been shown that shared entanglement and quantum operations can aid the players to coordinate their actions and acquire higher payoffs than is possible with classical randomization. In this paper the initial quantum state is expanded to a family of GHZ-type states and strategies are discussed in terms of possible final outcomes. It is shown that the players individually seek outcomes that maximize the collective good.