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Journal of Southwest China Normal University

The Effect on The Expected Payoff of Corrupted Three-player Quantum Prisoner's Dilemma

Nie Jing

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

The Prisoner's Dilemma plays a very important part in the game theory.It is related to economics,political science,sociology,philosophy,ethnics,etc.when study in such field quantized the Prisoner's Dilemma and found that the payoffs for the players are better than that in the classical game.Then,people developed the two-player Quantum Prisoner's Dilemma into multiplayer quantum game.Also,they found that the quantum game does better than classical game.But now,the quantum advantage arising in a simplified multiplayer quantum game is found to be disadvantage when the game's qubit source is corrupted.

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The Prisoner's Dilemma plays a very important part in the game theory.It is related to economics,political science,sociology,philosophy,ethnics,etc.when study in such field quantized the Prisoner's Dilemma and found that the payoffs for the players are better than that in the classical game.Then,people developed the two-player Quantum Prisoner's Dilemma into multiplayer quantum game.Also,they found that the quantum game does better than classical game.But now,the quantum advantage arising in a simplified multiplayer quantum game is found to be disadvantage when the game's qubit source is corrupted.
In this paper, we extend the quantum game theory of Prisoner’s Dilemma to the N-player case. The final state of quantum game theory of N-player Prisoner’s Dilemma is derived, which can be used to investigate the payoff of each player. As demonstration, two cases (2-player and 3-player) are studied to illustrate the superiority of quantum strategy in the game theory. Specifically, the non-unique entanglement parameter is found to maximize the total payoff, which oscillates periodically. Finally, the optimal strategic set is proved to depend on the selection of initial states.
We study the three-player prisoner's dilemma game under the effect of decoherence and correlated noise. It is seen that the quantum player is always better off than the classical players. It is also seen that the game's Nash equilibrium does not change in the presence of correlated noise in contradiction to the effect of decoherence in the multiplayer case. Furthermore, it is shown that for maximum correlation the game does not behave as a noiseless game and the quantum player is still better off for all values of the decoherence parameter p which is not possible in the two-player case. In addition, the payoffs reduction due to decoherence is controlled by the correlated noise throughout the course of the game.
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.