Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0510108 · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Multiplayer quantum Minority game with decoherence

Adrian P. Flitney

Published May 23, 2005• 8 citations
arXivHTMLPDF

Abstract

A quantum version of the Minority game for an arbitrary number of agents is studied. When the number of agents is odd, quantizing the game produces no advantage to the players, however, for an even number of agents new Nash equilibria appear that have no classical analogue. The new Nash equilibria provide far preferable expected payoffs to the players compared to the equivalent classical game. The effect on the Nash equilibrium payoff of reducing the degree of entanglement, or of introducing decoherence into the model, is indicated.

DOI
10.1117/12.609363

Related papers

Multiplayer quantum minority game with decoherence

Adrian P. Flitney, Lloyd C. L. Hollenberg

A quantum version of the Minority game for an arbitrary number of agents is studied. When the number of agents is odd, quantizing the game produces no advantage to the players, however, for an even number of agents new Nash equilibria appear that have no classical analogue. The new Nash equilibria provide far preferable expected payoffs to the players compared to the equivalent classical game. The effect on the Nash equilibrium payoff of reducing the degree of initial entanglement between the players' qubits or of introducing various forms of decoherence is discussed. As the number of players increases the multipartite GHZ state becomes increasingly fragile, as indicated by the smaller error probability required to reduce the Nash equilibrium payoff to the classical level.

Quantum Information and Computation•Jan 1, 2007•31 citations

Multiplayer quantum minority game with decoherence

Adrian P. Flitney, Lloyd C. L. Hollenberg

A quantum version of the Minority game for an arbitrary number of agents is considered. It is known that when the number of agents is odd, quantizing the game produces no advantage to the players, but for an even number of agents new Nash equilibria appear that have no classical analogue and have improved payoffs. We study the effect on the Nash equilibrium payoff of various forms of decoherence. As the number of players increases the multipartite GHZ state becomes increasingly fragile, as indicated by the smaller error probability required to reduce the Nash equilibrium payoff to the classical level.

Quantum Information and Computation•Jan 1, 2007•12 citations

The effect of quantum noise on multiplayer quantum game

Cao Shuai, Fang Mao-Fa, Zheng Xiao-Juan

It has recently been realized that quantum strategies have a great advantage over classical ones in quantum games. However, quantum states are easily affected by the quantum noise, resulting in decoherence. In this paper, we investigate the effect of quantum noise on a multiplayer quantum game with a certain strategic space, with all players affected by the same quantum noise at the same time. Our results show that in a maximally entangled state, a special Nash equilibrium appears in the range of 0≤p≤0.622 (p is the quantum noise parameter), and then disappears in the range of 0.622<p≤1. Increasing the amount of quantum noise leads to the reduction of the quantum player's payoff.

Chinese Physics•Mar 20, 2007•9 citations

Quantum minority game utilizing various forms of entanglement

Adrian P. Flitney, Lloyd C. L. Hollenberg

The quantum Minority game provides a means of studying the effect of multi-partite entanglement in a game theoretic setting. We study symmetric Nash equilibria and symmetric Pareto optimal strategies arising in a four-player quantum Minority game that uses an initial state that is a superposition of a GHZ state and products of EPR pairs. We find that the payoff curve for the symmetric Pareto optimal strategy is the same as that for the maximal violation of the Mermin-Ardehali-Belinskii-Klyshko inequality for the initial state, indicating a correspondence between quantum game theory and Bell inequalities. We also show that no advantage over the classical Minority game can be obtained when the initial state has only two party entanglement.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Dec 3, 2007•4 citations

The effect of quantum noise on the restricted quantum game

Cao Shuai, Mao-Fa Fang

It has recently been established that quantum strategies have great advantage over classical ones in quantum games. However, quantum states are easily affected by the quantum noise resulting in decoherence. In this paper, we investigate the effect of quantum noise on the restricted quantum game in which one player is restricted in classical strategic space, another in quantum strategic space and only the quantum player is affected by the quantum noise. Our results show that in the maximally entangled state, no Nash equilibria exist in the range of 0< p ⩽0.422 ( p is the quantum noise parameter), while two special Nash equilibria appear in the range of 0.422< p <1. The advantage that the quantum player diminished only in the limit of maximum quantum noise. Increasing the amount of quantum noise leads to the increase of the classical player's payoff and the reduction of the quantum player's payoff, but is helpful in forming two Nash equilibria.

Chinese Physics•Jan 1, 2006•5 citations

Classification of Nash Equilibria inQuantum Games

Yoshitaka Sakagami

Abstract We consider general quantum two-player games and investigate the effect of the degree of entanglement on Nash equilibria. The strategy set is SU(2). Each player's payoffs of the payoff table are different from each other. The purpose of this paper is to classify Nash equilibria by their payoff patterns. We derive all different payoff patterns of Nash equlibria which may occur. Further, for each payoff pattern, we derive all Nash equilibria for which this pattern occurs.

•Aug 28, 2023•0 citations
A quantum version of the Minority game for an arbitrary number of agents is studied. When the number of agents is odd, quantizing the game produces no advantage to the players, however, for an even number of agents new Nash equilibria appear that have no classical analogue. The new Nash equilibria provide far preferable expected payoffs to the players compared to the equivalent classical game. The effect on the Nash equilibrium payoff of reducing the degree of entanglement, or of introducing decoherence into the model, is indicated.
A quantum version of the Minority game for an arbitrary number of agents is studied. When the number of agents is odd, quantizing the game produces no advantage to the players, however, for an even number of agents new Nash equilibria appear that have no classical analogue. The new Nash equilibria provide far preferable expected payoffs to the players compared to the equivalent classical game. The effect on the Nash equilibrium payoff of reducing the degree of initial entanglement between the players' qubits or of introducing various forms of decoherence is discussed. As the number of players increases the multipartite GHZ state becomes increasingly fragile, as indicated by the smaller error probability required to reduce the Nash equilibrium payoff to the classical level.
A quantum version of the Minority game for an arbitrary number of agents is considered. It is known that when the number of agents is odd, quantizing the game produces no advantage to the players, but for an even number of agents new Nash equilibria appear that have no classical analogue and have improved payoffs. We study the effect on the Nash equilibrium payoff of various forms of decoherence. As the number of players increases the multipartite GHZ state becomes increasingly fragile, as indicated by the smaller error probability required to reduce the Nash equilibrium payoff to the classical level.
It has recently been realized that quantum strategies have a great advantage over classical ones in quantum games. However, quantum states are easily affected by the quantum noise, resulting in decoherence. In this paper, we investigate the effect of quantum noise on a multiplayer quantum game with a certain strategic space, with all players affected by the same quantum noise at the same time. Our results show that in a maximally entangled state, a special Nash equilibrium appears in the range of 0≤p≤0.622 (p is the quantum noise parameter), and then disappears in the range of 0.622<p≤1. Increasing the amount of quantum noise leads to the reduction of the quantum player's payoff.
The quantum Minority game provides a means of studying the effect of multi-partite entanglement in a game theoretic setting. We study symmetric Nash equilibria and symmetric Pareto optimal strategies arising in a four-player quantum Minority game that uses an initial state that is a superposition of a GHZ state and products of EPR pairs. We find that the payoff curve for the symmetric Pareto optimal strategy is the same as that for the maximal violation of the Mermin-Ardehali-Belinskii-Klyshko inequality for the initial state, indicating a correspondence between quantum game theory and Bell inequalities. We also show that no advantage over the classical Minority game can be obtained when the initial state has only two party entanglement.
It has recently been established that quantum strategies have great advantage over classical ones in quantum games. However, quantum states are easily affected by the quantum noise resulting in decoherence. In this paper, we investigate the effect of quantum noise on the restricted quantum game in which one player is restricted in classical strategic space, another in quantum strategic space and only the quantum player is affected by the quantum noise. Our results show that in the maximally entangled state, no Nash equilibria exist in the range of 0< p ⩽0.422 ( p is the quantum noise parameter), while two special Nash equilibria appear in the range of 0.422< p <1. The advantage that the quantum player diminished only in the limit of maximum quantum noise. Increasing the amount of quantum noise leads to the increase of the classical player's payoff and the reduction of the quantum player's payoff, but is helpful in forming two Nash equilibria.