Quantum games and quantum strategies

Quantum games and quantum strategies

March 16, 2020 | Jens Eisert, Martin Wilkens, and Maciej Lewenstein
This paper investigates the quantization of non-zero sum games, focusing on the Prisoners' Dilemma. It shows that quantum strategies can resolve the dilemma, as mutual cooperation becomes beneficial. The authors construct a quantum strategy that always yields a reward when played against any classical strategy. They propose a physical model of the game, where players use quantum strategies to maximize their payoffs. The game is modeled using quantum mechanics, with players' strategies represented by unitary operators acting on qubits. The paper demonstrates that quantum strategies can lead to new Nash equilibria, such as $\hat{Q} \otimes \hat{Q}$, which is Pareto optimal and ensures mutual benefit. The authors also show that quantum strategies can outperform classical strategies in certain scenarios, particularly when entanglement is present. They argue that quantum mechanics allows for more efficient game implementations, especially in environments with limited resources. The paper also discusses the implications of quantum strategies in unfair games, where one player can exploit the other's classical strategies. The results highlight the potential of quantum mechanics to enhance strategic decision-making in games.This paper investigates the quantization of non-zero sum games, focusing on the Prisoners' Dilemma. It shows that quantum strategies can resolve the dilemma, as mutual cooperation becomes beneficial. The authors construct a quantum strategy that always yields a reward when played against any classical strategy. They propose a physical model of the game, where players use quantum strategies to maximize their payoffs. The game is modeled using quantum mechanics, with players' strategies represented by unitary operators acting on qubits. The paper demonstrates that quantum strategies can lead to new Nash equilibria, such as $\hat{Q} \otimes \hat{Q}$, which is Pareto optimal and ensures mutual benefit. The authors also show that quantum strategies can outperform classical strategies in certain scenarios, particularly when entanglement is present. They argue that quantum mechanics allows for more efficient game implementations, especially in environments with limited resources. The paper also discusses the implications of quantum strategies in unfair games, where one player can exploit the other's classical strategies. The results highlight the potential of quantum mechanics to enhance strategic decision-making in games.
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