AI summary · arXiv: 2211.01687v3 · quant-ph
Improving social welfare in non-cooperative games with different types of quantum resources
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How Quantum Information Can Improve Social WelfareB. Groisman, Michael McGettrick, M. Mhalla et al. · 2019 · IEEE Journal on Selected Areas in Information Theory · cited 4 times · Not summarized yet
Abstract
It is known that quantum resources can allow us to achieve a family of equilibria that can have sometimes a better social welfare, while guaranteeing privacy. We use graph games to propose a way to build non-cooperative games from graph states, and we show how to achieve an unlimited improvement with quantum advice compared to classical advice.
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Quantum strategic game theorySheng-Yu Zhang · 2010 · Information Technology Convergence and Services · cited 74 times · Not summarized yet
Abstract
We propose a simple yet rich model to extend strategic games to the quantum setting, in which we define quantum Nash and correlated equilibria and study the relations between classical and quantum equilibria. Unlike all previous work that focused on qualitative questions on specific games of very small sizes, we quantitatively address the following fundamental question for general games of growing sizes: How much "advantage" can playing quantum strategies provide, if any? Two measures of the advantage are studied. 1. Since game mainly is about each player trying to maximize individual payoff, a natural measure is the increase of payoff by playing quantum strategies. We consider natural mappi…
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Nonlocal correlations: Fair and unfair strategies in Bayesian gamesArup Roy, Amit Mukherjee, Tamal Guha et al. · 2016 · Physical Review A · cited 48 times · Not summarized yet
Abstract
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 classical equilibrium strategies in common interest Bayesian games and also in conflicting interest games. However, classical equilibrium strategies can be of two types, fair and unfair. Whereas in fair equilibrium payoffs of different players are same, in unfair case they differ. Advantage of nonlocal correlation has been demonstrated over fair strategies. In this work we show that quantum strategies can outperform even the unfair classical equilibrium strategies. For thi…
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Playing Bayesian games better with separable quantum states than with any classical correlationY. Wang, G. Scarpa, A. Winter · 2026 · Not summarized yet
Abstract
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, eve…
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Nonlocality and conflicting interest games.A. Pappa, Niraj Kumar, T. Lawson et al. · 2014 · Physical Review Letters · cited 75 times · Not summarized yet
Abstract
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 …
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Belief-invariant and quantum equilibria in games of incomplete informationV. Auletta, Diodato Ferraioli, Ashutosh Rai et al. · 2016 · Theoretical Computer Science · cited 16 times · Not summarized yet
Abstract
Drawing on ideas from game theory and quantum physics, we investigate nonlocal correlations from the point of view of equilibria in games of incomplete information. These equilibria can be classified in decreasing power as general communication equilibria, belief-invariant equilibria and correlated equilibria, all of which contain the familiar Nash equilibria. The notion of belief-invariant equilibrium has appeared in game theory before, in the 1990s. However, the class of non-signalling correlations associated to belief-invariance arose naturally already in the 1980s in the foundations of quantum mechanics. Here, we explain and unify these two origins of the idea and study the above classes…
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Three-player conflicting interest games and nonlocalityK. Bolonek-Lasoń · 2016 · Quantum Information Processing · cited 8 times · Not summarized yet
Abstract
We outline the general construction of three-player games with incomplete information which fulfil the following conditions: (i) symmetry with respect to the permutations of players; (ii) the existence of an upper bound for total payoff resulting from Bell inequalities; (iii) the existence of both fair and unfair Nash equilibria saturating this bound. Conditions (i)–(iii) imply that we are dealing with conflicting interest games. An explicit example of such a game is given. A quantum counterpart of this game is considered. It is obtained by keeping the same utilities but replacing classical advisor by a quantum one. It is shown that the quantum game possesses only fair equilibria with strict…
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Quantum Bayes Correlated Equilibrium and the Comparison of Quantum Information Structures in GamesFurkan Sezer · 2026 · cited 1 time · Not summarized yet
Abstract
Bergemann and Morris (2016) show that one information structure is more informative than another exactly when it induces a smaller set of Bayes correlated equilibrium outcomes in every game. We build the quantum analogue. An information structure becomes a family of density operators indexed by the payoff state, which the mediator observes. We show that obedience is equivalent to a Loewner domination between operators on one player's subsystem. The equilibrium set is then a nonempty compact spectrahedron computable by semidefinite programming, classical structures embed exactly, and under quantum individual sufficiency more information shrinks the equilibrium set in every game.
Prior work it builds on
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Contextuality in Multipartite Pseudo-Telepathy Graph GamesAnurag Anshu, Peter Høyer, M. Mhalla et al. · 2016 · International Symposium on Fundamentals of Computation Theory · cited 9 times · Not summarized yet
Abstract
Analyzing pseudo-telepathy graph games, we propose a way to build contextuality scenarios exhibiting the quantum supremacy using graph states. We consider the combinatorial structures generating equivalent scenarios. We introduce a new tool called multipartiteness width to investigate which scenarios are harder to decompose and show that there exist graphs generating scenarios with a linear multipartiteness width.
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Quantum games: a review of the history, current state, and interpretationFaisal Shah Khan, Neal Solmeyer, R. Balu et al. · 2018 · Quantum Information Processing · cited 133 times · Not summarized yet
Abstract
We review both theoretical and experimental developments in the area of quantum games since the inception of the subject circa 1999. We will also offer a narrative on the controversy that surrounded the subject in its early days, and how this controversy has affected the development of the subject.
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A convergent hierarchy of semidefinite programs characterizing the set of quantum correlationsMiguel Navascués, Stefano Pironio, Antonio Acín · 2008 · New Journal of Physics · cited 368 times · Not summarized yet
Abstract
We are interested in the problem of characterizing the correlations that arise when performing local measurements on separate quantum systems. In a previous work (Navascués et al 2007 Phys. Rev. Lett. 98 010401), we introduced an infinite hierarchy of conditions necessarily satisfied by any set of quantum correlations. Each of these conditions could be tested using semidefinite programming. We present here new results concerning this hierarchy. We prove in particular that it is complete, in the sense that any set of correlations satisfying every condition in the hierarchy has a quantum representation in terms of commuting measurements. Although our tests are conceived to rule out non-quantum…
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Bell inequalities and entanglementR. Werner, M. M. Wolf · 2001 · Quantum information & computation · cited 268 times · Not summarized yet
Abstract
We discuss general Bell inequalities for bipartite and multipartite systems, emphasizing the connection with convex geometry on the mathematical side, and the communication aspects on the physical side. Known results on families of generalized Bell inequalities are summarized. We investigate maximal violations of Bell inequalities as well as states not violating (certain) Bell inequalities. Finally, we discuss the relation between Bell inequality violations and entanglement properties currently discussed in quantum information theory.
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Scalable Bell Inequalities for Qubit Graph States and Robust Self-Testing.F. Baccari, R. Augusiak, Ivan Šupić et al. · 2018 · Physical Review Letters · cited 83 times · Not summarized yet
Abstract
Bell inequalities constitute a key tool in quantum information theory: they not only allow one to reveal nonlocality in composite quantum systems, but, more importantly, they can be used to certify relevant properties thereof. We provide a general construction of Bell inequalities that are maximally violated by the multiqubit graph states and can be used for their robust self-testing. Apart from their theoretical relevance, our inequalities offer two main advantages from an experimental viewpoint: (i) they present a significant reduction of the experimental effort needed to violate them, as the number of correlations they contain scales only linearly with the number of observers; (ii) numeri…
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