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

Nash Equilibrium in Quantum Games

J Du, Ruitian Han, H Li, Xiaoyang Xu, Xiaoqi Zhou

Published Oct 12, 2000• 3 citations
OpenAlex

Abstract

We investigate Nash Equilibrium in quantum games by quantizing the Battle of Sexes Game, finding that there is no unique but infinite Nash Equilibrium in it. A method is also provided to check that whether a quantum game has unique Nash Equilibrium, which could be helpful for multi-player quantum games.

Related papers

Nash Equilibrium in the Quantum Battle of Sexes Game

Jiangfeng Du, Xiaodong Xu, Li, Hui +2 more

We investigate Nash Equilibrium in the quantum Battle of Sexes Game. We find the game has infinite Nash Equilibria and all of them leads to the asymmetry result. We also show that there is no unique but infinite Nash Equilibrium in it if we use the quantizing scheme proposed by Eisert et al and the two players are allowed to adopt any unitary operator as his/her strategies.

arXiv:quant-ph/0010050•Oct 12, 2000•13 citations

Multiple Nash-equilibrium in Quantum Game

G. N. Parfionov

Methods of exploring Nash equilibrium in quantum games are studied. Analytical conditions of the existence, the uniqueness or the multiplicity of the equilibria are found.

arXiv:0806.1102•Jun 6, 2008•3 citations

Quantum Battle of the Sexes Revisited

de Farias Neto, João José Neto

Several quantum versions of the battle of the sexes game are analyzed. Some of them are shown to reproduce the classical game. In some, there are no Nash quantum pure equilibria. In some others, the payoffs are always equal to each other. In others still, all equilibria favor Alice or Bob depending on a phase shift of the initial state of the system. Explicit detailed calculations are for the first time exhibited.

arXiv:quant-ph/0408019•Aug 3, 2004•3 citations

No fixed-point guarantee of Nash equilibrium in quantum games

Faisal Shah Khan, Travis S. Humble

The theory of quantum games permits players to choose strategies that prepare and measure quantum states. Whereas conventional game theory provides guarantees for fixed-point stability in non-cooperative games, so-called Nash equilibria, we find this guarantee is not provided for quantum games. In particular, we show the conditions for Glickberg's fixed-point theorem do not apply to pure quantum games when the payoff is a physical observable. We further show that Nash equilibrium can be guaranteed when the payoff is defined with respect to state preparation.

arXiv:1609.08360•Sep 27, 2016•1 citation

Quantum Game in Matrix Strategies

Ying-Jun Ma, Gui‐Lu Long

We study a quantum game played by two players with restricted multiple strategies. It is found that in quantum game Nash equilibrium does not always exist which is totally different from that in classical game. This happens only when the initial state is in entangled state. At the same time, we find that when Nash equilibrium exists the pay off function is usually different from that in the classical counterpart except in some special cases. This presents an explicit example where quantum game and classical game differ fundamentally.

•Jan 15, 2003•1 citation

Nash Embedding and Equilibrium in Pure Quantums States

Faisal Shah Khan, Travis S. Humble

With respect to probabilistic mixtures of the strategies in non-cooperative games, quantum game theory provides guarantee of fixed-point stability, the so-called Nash equilibrium. This permits players to choose mixed quantum strategies that prepare mixed quantum states optimally under constraints. We show here that fixed-point stability of Nash equilibrium can also be guaranteed for pure quantum strategies via an application of the Nash embedding theorem, permitting players to prepare pure quantum states optimally under constraints.

•Aug 1, 2018•0 citations
The theory of quantum games permits players to choose strategies that prepare and measure quantum states. Whereas conventional game theory provides guarantees for fixed-point stability in non-cooperative games, so-called Nash equilibria, we find this guarantee is not provided for quantum games. In particular, we show the conditions for Glickberg's fixed-point theorem do not apply to pure quantum games when the payoff is a physical observable. We further show that Nash equilibrium can be guaranteed when the payoff is defined with respect to state preparation.
We study a quantum game played by two players with restricted multiple strategies. It is found that in quantum game Nash equilibrium does not always exist which is totally different from that in classical game. This happens only when the initial state is in entangled state. At the same time, we find that when Nash equilibrium exists the pay off function is usually different from that in the classical counterpart except in some special cases. This presents an explicit example where quantum game and classical game differ fundamentally.
With respect to probabilistic mixtures of the strategies in non-cooperative games, quantum game theory provides guarantee of fixed-point stability, the so-called Nash equilibrium. This permits players to choose mixed quantum strategies that prepare mixed quantum states optimally under constraints. We show here that fixed-point stability of Nash equilibrium can also be guaranteed for pure quantum strategies via an application of the Nash embedding theorem, permitting players to prepare pure quantum states optimally under constraints.