# Multiplayer quantum games

@article{Benjamin2001MultiplayerQG, title={Multiplayer quantum games}, author={S. Benjamin and P. Hayden}, journal={Physical Review A}, year={2001}, volume={64}, pages={030301} }

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

#### 248 Citations

Network Games with Quantum Strategies

- 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

- Physics
- 2007

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… Expand

An Introductory Review on Quantum Game Theory

- Mathematics
- 2010 Fourth International Conference on Genetic and Evolutionary Computing
- 2010

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 classical… Expand

Quantum Locality in Game Strategy

- Physics, Mathematics
- Scientific reports
- 2017

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

- Physics
- 2002

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 particular… Expand

Cooperative quantum Parrondo’s games

- Mathematics, Physics
- 2013

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 interesting… Expand

A quantum extension to inspection game

- Computer Science
- ArXiv
- 2015

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

- Computer Science
- Quantum Inf. Process.
- 2019

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

- Physics, Mathematics
- 2008

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 and… Expand

Advantage of a quantum player over a classical one in 2 × 2 quantum games

- 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

#### References

SHOWING 1-10 OF 11 REFERENCES

QUANTUM GAMES AND QUANTUM ALGORITHMS

- Mathematics, Physics
- 2000

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 formalize… Expand

Quantum strategies

- Computer Science, Physics
- 1998

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

- Physics
- 1999

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 also… Expand

Quantum games

- Physics
- 2000

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

- Computer Science
- 1999

The best way to win a game like 'paper-stone-scissors' is to use "quantum rules", says Phil Ball. Expand

Schrodinger's Games.

- Physics
- 2000

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 of… Expand

Comment on "quantum games and quantum strategies".

- Physics, Medicine
- Physical review letters
- 2001

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

- 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 predictions… Expand

Phage-lift for game theory

- Economics, Medicine
- Nature
- 1999

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 virus… Expand

States, effects, and operations : fundamental notions of quantum theory : lectures in mathematical physics at the University of Texas at Austin

- Mathematics
- 1983

States and effects.- Operations.- The first Representation theorem.- Composite systems.- The second representation theorem.- 6 Coexistent effects and observables.- References.