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:1705.04639 · Physical Review A

Strong quantum solutions in conflicting-interest Bayesian games

Ashutosh Rai, Goutam Paul

Published Oct 30, 2017• 10 citations
arXivHTMLPDF

Abstract

Quantum entanglement has been recently demonstrated as a useful resource in conflicting-interest games of incomplete information between two players, Alice and Bob [Pappa et al., Phys. Rev. Lett. 114, 020401 (2015)]. The general setting for such games is that of correlated strategies where the correlation between competing players is established through a trusted common adviser; however, players need not reveal their input to the adviser. So far, the quantum advantage in such games has been revealed in a restricted sense. Given a quantum correlated equilibrium strategy, one of the players can still receive a higher than quantum average payoff with some classically correlated equilibrium strategy. In this work, by considering a class of asymmetric Bayesian games, we show the existence of games with quantum correlated equilibrium where the average payoff of both the players exceeds the respective individual maximum for each player over all classically correlated equilibriums.

DOI
10.1103/physreva.96.042340

Related papers

Nonlocal correlations: Fair and Unfair Strategies in Conflicting Bayesian Game

Arup Roy, Amit Mukherjee, Tamal Guha +3 more

Interesting connection has been established between two apparently unrelated concepts, namely, quantum nonlocality and Bayesian game theory. It has been shown that nonlocal correlations in the form of advice can outperform the best classical strategies in common interest Bayesian games and can also surpass the fair classical equilibrium payoffs in conflicting games. However a conflicting game may have unfair equilibrium strategies, which are the archetypal of such games and never occur in common interest games. In this work, making the connection between nonlocality and Bayesian game more striking, we show that quantum strategies can outperform even the unfair classical equilibrium strategies in conflicting games. For this purpose here we consider the conflicting game proposed in [Phys. Rev. Lett. 114, 020401 (2015)]. Moreover, we provide a complete characterization of the nonlocal correlations that are advantageous over the best fair and unfair classical strategies in the said game.

•Jan 11, 2016•0 citations

Nonlocality, entanglement, and randomness in different conflicting interest Bayesian games

Hargeet Kaur, Atul Kumar

We analyse different Bayesian games where payoffs of players depend on the types of players involved in a two-player game. The dependence is assumed to commensurate with the CHSH game setting. For this, we consider two different types of each player (Alice and Bob) in the game, thus resulting in four different games clubbed together as one Bayesian game. Considering different combinations of common interest, and conflicting interest coordination and anti-coordination games, we find that quantum strategies are always preferred over classical strategies if the shared resource is a pure non-maximally entangled state. However, when the shared resource is a class of mixed state, then quantum strategies are useful only for a given range of the state parameter. Surprisingly, when all conflicting interest games (Battle of the Sexes game and Chicken game) are merged into the Bayesian game picture, then the best strategy for Alice and Bob is to share a set of non-maximally entangled pure states. We demonstrate that this set not only gives higher payoff than any classical strategy, but also outperforms a maximally entangled pure Bell state, mixed Werner states, and Horodecki states. We further propose the representation of a special class of Bell inequality- tilted Bell inequality, as a common as well as conflicting interest Bayesian game. We thereafter, study the effect of sharing an arbitrary two-qubit pure state and a class of mixed state as quantum resource in those games; thus verifying that non-maximally entangled states with high randomness help attain maximum quantum benefit. Additionally, we propose a general framework of a two-player Bayesian game for d-dimensions Bell-CHSH inequality, with and without the tilt factor.

Quantum Information and Computation•Sep 1, 2020•2 citations

Playing Bayesian Games with General Quantum Advice

Xiaozhen Ge, Zairong Xi

The correlations, established through quantum sources, have been demonstrated to outperform classical ones in the game theory. As shown in the game firstly proposed in [Phys. Rev. Lett. 114, 020401 (2015)], the considered conflicting Bayesian game can be converted into a common interest one and end in a better solution than all classical possible when the players share a maximally entangled state. In this paper, motivated by the possible constraints on the states in practical applications, we would like to discuss more general quantum advice and analyze the effects on the aforementioned Bayesian game.

Chinese Control Conference (CCC)•Jul 1, 2018•0 citations

Characterizing the Nash equilibria of three-player Bayesian quantum games

Neal Solmeyer, Radhakrishnan Balu

Quantum games with incomplete information can be studied within a Bayesian framework. We analyze games quantized within the EWL framework [Eisert, Wilkens, and Lewenstein, Phys Rev. Lett. 83, 3077 (1999)]. We solve for the Nash equilibria of a variety of two-player quantum games and compare the results to the solutions of the corresponding classical games. We then analyze Bayesian games where there is uncertainty about the player types in two-player conflicting interest games. The solutions to the Bayesian games are found to have a phase diagram-like structure where different equilibria exist in different parameter regions, depending both on the amount of uncertainty and the degree of entanglement. We find that in games where a Pareto-optimal solution is not a Nash equilibrium, it is possible for the quantized game to have an advantage over the classical version. In addition, we analyze the behavior of the solutions as the strategy choices approach an unrestricted operation. We find that some games have a continuum of solutions, bounded by the solutions of a simpler restricted game. A deeper understanding of Bayesian quantum game theory could lead to novel quantum applications in a multi-agent setting.

arXiv:1703.03292•Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 5, 2017•7 citations

Playing Bayesian games better with separable quantum states than with any classical correlation

Yaqing Xy Wang, Giannicola Scarpa, Andreas Winter

Bayesian games, also known as games of incomplete information, are a fruitful arena for exploring the impact of correlations on a set of independent agents (players) via the game equilibria to which they give rise. It was realised some time ago that quantum states shared between the players can lead to new and beneficial equilibria, compared to classical correlation. While until now examples of this effect required an entangled state, here we show that even separable states can create new, genuinely quantum equilibria in games, that are advantageous with respect to all classically correlated equilibria. This shows that non-classical correlations beyond entanglement are indeed a resource, even in otherwise entirely classical situations. Our result brings quantum advantage in games significantly closer to possible realisation.

quant-pharXiv:2607.09477•Jul 13, 2026•0 citations

Nonlocality and Conflicting Interest Games

Anna Pappa, Niraj Kumar, Thomas Lawson +4 more

Nonlocality enables two parties to win specific games with probabilities strictly higher than allowed by any classical theory. Nevertheless, all known such examples consider games where the two parties have a common interest, since they jointly win or lose the game. The main question we ask here is whether the nonlocal feature of quantum mechanics can offer an advantage in a scenario where the two parties have conflicting interests. We answer this in the affirmative by presenting a simple conflicting interest game, where quantum strategies outperform classical ones. Moreover, we show that our game has a fair quantum equilibrium with higher payoffs for both players than in any fair classical equilibrium. Finally, we play the game using a commercial entangled photon source and demonstrate experimentally the quantum advantage.

arXiv:1408.3281•Physical Review Letters•Jan 14, 2015•70 citations
Quantum entanglement has been recently demonstrated as a useful resource in conflicting-interest games of incomplete information between two players, Alice and Bob [Pappa et al., Phys. Rev. Lett. 114, 020401 (2015)]. The general setting for such games is that of correlated strategies where the correlation between competing players is established through a trusted common adviser; however, players need not reveal their input to the adviser. So far, the quantum advantage in such games has been revealed in a restricted sense. Given a quantum correlated equilibrium strategy, one of the players can still receive a higher than quantum average payoff with some classically correlated equilibrium strategy. In this work, by considering a class of asymmetric Bayesian games, we show the existence of games with quantum correlated equilibrium where the average payoff of both the players exceeds the respective individual maximum for each player over all classically correlated equilibriums.
Interesting connection has been established between two apparently unrelated concepts, namely, quantum nonlocality and Bayesian game theory. It has been shown that nonlocal correlations in the form of advice can outperform the best classical strategies in common interest Bayesian games and can also surpass the fair classical equilibrium payoffs in conflicting games. However a conflicting game may have unfair equilibrium strategies, which are the archetypal of such games and never occur in common interest games. In this work, making the connection between nonlocality and Bayesian game more striking, we show that quantum strategies can outperform even the unfair classical equilibrium strategies in conflicting games. For this purpose here we consider the conflicting game proposed in [Phys. Rev. Lett. 114, 020401 (2015)]. Moreover, we provide a complete characterization of the nonlocal correlations that are advantageous over the best fair and unfair classical strategies in the said game.
We analyse different Bayesian games where payoffs of players depend on the types of players involved in a two-player game. The dependence is assumed to commensurate with the CHSH game setting. For this, we consider two different types of each player (Alice and Bob) in the game, thus resulting in four different games clubbed together as one Bayesian game. Considering different combinations of common interest, and conflicting interest coordination and anti-coordination games, we find that quantum strategies are always preferred over classical strategies if the shared resource is a pure non-maximally entangled state. However, when the shared resource is a class of mixed state, then quantum strategies are useful only for a given range of the state parameter. Surprisingly, when all conflicting interest games (Battle of the Sexes game and Chicken game) are merged into the Bayesian game picture, then the best strategy for Alice and Bob is to share a set of non-maximally entangled pure states. We demonstrate that this set not only gives higher payoff than any classical strategy, but also outperforms a maximally entangled pure Bell state, mixed Werner states, and Horodecki states. We further propose the representation of a special class of Bell inequality- tilted Bell inequality, as a common as well as conflicting interest Bayesian game. We thereafter, study the effect of sharing an arbitrary two-qubit pure state and a class of mixed state as quantum resource in those games; thus verifying that non-maximally entangled states with high randomness help attain maximum quantum benefit. Additionally, we propose a general framework of a two-player Bayesian game for d-dimensions Bell-CHSH inequality, with and without the tilt factor.
The correlations, established through quantum sources, have been demonstrated to outperform classical ones in the game theory. As shown in the game firstly proposed in [Phys. Rev. Lett. 114, 020401 (2015)], the considered conflicting Bayesian game can be converted into a common interest one and end in a better solution than all classical possible when the players share a maximally entangled state. In this paper, motivated by the possible constraints on the states in practical applications, we would like to discuss more general quantum advice and analyze the effects on the aforementioned Bayesian game.
Quantum games with incomplete information can be studied within a Bayesian framework. We analyze games quantized within the EWL framework [Eisert, Wilkens, and Lewenstein, Phys Rev. Lett. 83, 3077 (1999)]. We solve for the Nash equilibria of a variety of two-player quantum games and compare the results to the solutions of the corresponding classical games. We then analyze Bayesian games where there is uncertainty about the player types in two-player conflicting interest games. The solutions to the Bayesian games are found to have a phase diagram-like structure where different equilibria exist in different parameter regions, depending both on the amount of uncertainty and the degree of entanglement. We find that in games where a Pareto-optimal solution is not a Nash equilibrium, it is possible for the quantized game to have an advantage over the classical version. In addition, we analyze the behavior of the solutions as the strategy choices approach an unrestricted operation. We find that some games have a continuum of solutions, bounded by the solutions of a simpler restricted game. A deeper understanding of Bayesian quantum game theory could lead to novel quantum applications in a multi-agent setting.
Bayesian games, also known as games of incomplete information, are a fruitful arena for exploring the impact of correlations on a set of independent agents (players) via the game equilibria to which they give rise. It was realised some time ago that quantum states shared between the players can lead to new and beneficial equilibria, compared to classical correlation. While until now examples of this effect required an entangled state, here we show that even separable states can create new, genuinely quantum equilibria in games, that are advantageous with respect to all classically correlated equilibria. This shows that non-classical correlations beyond entanglement are indeed a resource, even in otherwise entirely classical situations. Our result brings quantum advantage in games significantly closer to possible realisation.
Nonlocality enables two parties to win specific games with probabilities strictly higher than allowed by any classical theory. Nevertheless, all known such examples consider games where the two parties have a common interest, since they jointly win or lose the game. The main question we ask here is whether the nonlocal feature of quantum mechanics can offer an advantage in a scenario where the two parties have conflicting interests. We answer this in the affirmative by presenting a simple conflicting interest game, where quantum strategies outperform classical ones. Moreover, we show that our game has a fair quantum equilibrium with higher payoffs for both players than in any fair classical equilibrium. Finally, we play the game using a commercial entangled photon source and demonstrate experimentally the quantum advantage.