Communication aspects of a three-player Prisoner's Dilemma quantum game

Abstract

We present a quantization scheme for a three-player Prisoner's Dilemma game. It is shown that entanglement plays a dominant role in the three-player quantum game. Four different types of payoffs are identified on the basis of different combinations of initial state and measurement basis entanglement parameters. A relation among these different payoffs is also established. We also study the communication aspects of the three-player game.By exploiting different combinations of initial state and measurement basis entanglement parameters, we establish a relationship for the information shared among the parties. It is seen that the strategies of the players act as carriers of information in quantum games.

Environment-Assisted Quantum Minority Games

“…During last few years, number of authors have contributed to the development of quantum game theory [3][4][5][6][7][8][9][10][11][12][13][14]. Several classical games have been converted into quantum domain such as quantum prisoners' dilemma [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”

Distinguishing quantum channels via magic squares game

“…During last few years, number of authors have contributed to the development of quantum game theory [4][5][6][7][8][9]. In this direction, much work has been done on quantum prisoners' dilemma game [10][11][12] and other games have been converted to the quantum realm including the battle of the sexes [8,13], the Monty Hall problem [14,15], the rock-scissors-paper [16], and the others [17][18][19][20]. Quantum pseudo-telepathy game [21] is something which can not be won in the classical world without communication but can be won in the quantum world using entangled state without any use of classical communication.…”

Noisy non-transitive quantum games

“…During last few years, tremendous efforts have been made towards the development of quantum game theory [6][7][8][9][10][11][12]. In this connection, much work has been devoted to convert the classical games into quantum domain such as prisoners' dilemma game [13][14][15] and many other games [16][17][18][19][20] involving two and three players. Quantum games with 3×3 payoff matrices and larger have have been discussed by Wang et al [21].…”