Abstract
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.
Highlights
We have illustrated the advantages of quantum strategy in game theory by introducing the 2-player and 3-player cases
The 3-player Prisoner’s Dilemma with different initial states is discussed and it has been found that the optimal strategic set depends on the selection of the initial state
From the point of view of the players, each of them can choose the optimal quantum strategy to maximize the payoff based on the initial state of the game
Summary
|0i and |1i in a 2-dimensional Hilbert space) in quantum game theory Each player in this quantum Prisoner’s Dilemma has their own qubit and can only manipulate it without communications. The quantum Prisoner’s Dilemma game has been proposed to study the food loss and waste in a two-echelon food supply chain [17] Both the classical game and the separable quantum game are proved to be useless for the Pareto optimal strategy. The 2-player Prisoner’s Dilemma is briefly discussed, and it is shown that the quantum strategy has no advantage without entanglement in the game. The total payoffs of the 3-player Prisoner’s Dilemma with respect to several parameters are extensively presented, including the initial state, the choices of other players, and the entanglement gate.
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