Quantum pseudo-telepathy games are good examples of explaining the strangeness of quantum mechanics and demonstrating the advantage of quantum resources over classical resources. Most of the quantu...
Quantum pseudo-telepathy games are good examples of explaining the strangeness of quantum mechanics and demonstrating the advantage of quantum resources over classical resources. Most of the quantum pseudo-telepathy games are common interest games, nevertheless conflicting interest games are more widely used to model real world situations. Recently Pappa et al. (Phys. Rev. Lett. 114, 020401, 2015) proposed the first two-party conflicting interest game where quantum advice enhances social optimality. In the present paper we give two new three-party conflicting interest games and show that quantum advice can enhance social optimality in a three-party setting. The first game we propose is based on the famous GHZ game which is a common interest game. The second game we propose is related to the Svetlichny inequality which demonstrates quantum mechanics cannot be explained by the local hidden variable model in a three-party setting.
The correlations, established through quantum sources, have been demonstrated to outperform classical ones in the game theory. As shown in the game firstly proposed in [Phys. Rev. Lett. 114, 020401 (2015)], the considered conflicting Bayesian game can be converted into a common interest one and end in a better solution than all classical possible when the players share a maximally entangled state. In this paper, motivated by the possible constraints on the states in practical applications, we would like to discuss more general quantum advice and analyze the effects on the aforementioned Bayesian game.