Multiplayer quantum games

  title={Multiplayer quantum games},
  author={S. Benjamin and P. Hayden},
  journal={Physical Review A},
Recently the concept of quantum information has been introduced into game theory. Here we present the first study of quantum games with more than two players. We discover that such games can possess an alternative form of equilibrium strategy, one which has no analog either in traditional games or even in two-player quantum games. In these ``coherent'' equilibria, entanglement shared among multiple players enables different kinds of cooperative behavior: indeed it can act as a contract, in the… Expand

Figures from this paper

Network Games with Quantum Strategies
  • G. Scarpa
  • Mathematics, Computer Science
  • QuantumComm
  • 2009
This work will aim to be a first step towards the merging of existing ideas, by studying the behavior of players in a quantum network, by showing that in some cases "classical" examples of inefficiency fail if players use quantum strategies. Expand
The effect of quantum noise on multiplayer quantum game
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 inExpand
An Introductory Review on Quantum Game Theory
With utilizing some quantum mechanism into the game theory, quantum game theory provides us with the ability to achieve results not otherwise possible. In this paper, a brief overview of classicalExpand
Quantum Locality in Game Strategy
It is shown that, for a bipartite non zero-sum game, input local quantum correlations, and separable states in particular, suffice to achieve an advantage over any strategy that uses classical resources, thus dispensing with quantum nonlocality, entanglement, or even discord between the players’ input states. Expand
Continuous-Variable Quantum Games
Abstract We investigate the quantization of games in which the players can access to a continuous set of classical strategies, making use of continuous-variable quantum systems. For the particularExpand
Cooperative quantum Parrondo’s games
Abstract Coordination and cooperation are among the most important issues of game theory. Recently, the attention turned to game theory on graphs and social networks. Encouraged by interestingExpand
A quantum extension to inspection game
This paper extends the classical inspection game into a quantum game version by quantizing the strategy space and importing entanglement between players and shows that the quantum inspection game has various Nash equilibria depending on the initial quantum state of the game. Expand
On collective quantum games
Four two- person game types are scrutinized by allowing the players to adopt the strategy of his best paid mate by paying particular attention to the effect of variable degree of entanglement on Nash equilibrium strategy pairs in fair games where both players are able to update their strategies. Expand
The effect of quantum memory on quantum games
We study quantum games with correlated noise through a generalized quantization scheme. We investigate the effects of memory on quantum games, such as Prisoner's Dilemma, Battle of the Sexes andExpand
Advantage of a quantum player over a classical one in 2 × 2 quantum games
  • A. Flitney, D. Abbott
  • Mathematics, Physics
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 2003
We study a general 2 × 2 symmetric entangled quantum game. When one player has access only to classical strategies, while the other can use the full range of quantum strategies, there are ‘miracle’Expand


A quantum algorithm for an oracle problem can be understood as a quantum strategy for a player in a two-player zero-sum game in which the other player is constrained to play classically. I formalizeExpand
Quantum strategies
It is proved that in general a quantum strategy is always at least as good as a classical one, and furthermore that when both players use quantum strategies there need not be any equilibrium, but if both are allowed mixed quantum strategiesthere must be. Expand
Quantum Games and Quantum Strategies
We investigate the quantization of non-zero sum games. For the particular case of the Prisoners' Dilemma we show that this game ceases to pose a dilemma if quantum strategies are allowed for. We alsoExpand
Quantum games
Abstract In these lecture notes we investigate the implications of the identification of strategies with quantum operations in game theory beyond the results presented Eisert et al. (1999, Phys. Rev.Expand
Everyone wins in quantum games
The best way to win a game like 'paper-stone-scissors' is to use "quantum rules", says Phil Ball. Expand
Schrodinger's Games.
Focuses on the theories of quantum mechanics underlying a paper in the October 11, 1999 'Physical Review Letters.' Discussion of 'Schrodinger's cat' as an example of quantum theory; The importance ofExpand
Comment on "quantum games and quantum strategies".
A Comment on the Letter by Jens Eisert, Martin Wilkens, and Maciej Lewenstein, Phys.Rev.Lett. 83, 3077 (1999). The authors of the Letter offer a Reply.
Quantum theory of probability and decisions
  • D. Deutsch
  • Mathematics, Physics
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1999
The probabilistic predictions of quantum theory are conventionally obtained from a special probabilistic axiom. But that is unnecessary because all the practical consequences of such predictionsExpand
Phage-lift for game theory
The prisoner's dilemma is a classic of game theory in which acting for individual advantage is pitted against acting for collective benefit. An example has been identified among clones of a virusExpand
States, effects, and operations : fundamental notions of quantum theory : lectures in mathematical physics at the University of Texas at Austin
States and effects.- Operations.- The first Representation theorem.- Composite systems.- The second representation theorem.- 6 Coexistent effects and observables.- References.