Strategies in Symmetric Kolkata Restaurant Problem

TL;DR

This paper explores quantum strategies in the symmetric Kolkata restaurant problem, demonstrating how entanglement and GHZ states can improve coordination and collective payoffs among players.

Contribution

It extends previous work by analyzing a family of GHZ-type states and discusses strategies that promote collective optimization in the quantum setting.

Findings

Shared entanglement enhances coordination

GHZ-type states improve collective payoffs

Players aim for outcomes maximizing the collective good

Abstract

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.