# N-Player Quantum Games in an EPR Setting

@article{Chappell2012NPlayerQG, title={N-Player Quantum Games in an EPR Setting}, author={James M. Chappell and Azhar Iqbal and Derek Abbott}, journal={PLoS ONE}, year={2012}, volume={7} }

The -player quantum games are analyzed that use an Einstein-Podolsky-Rosen (EPR) experiment, as the underlying physical setup. In this setup, a player’s strategies are not unitary transformations as in alternate quantum game-theoretic frameworks, but a classical choice between two directions along which spin or polarization measurements are made. The players’ strategies thus remain identical to their strategies in the mixed-strategy version of the classical game. In the EPR setting the quantum…

## 22 Citations

### The equivalence of Bell's inequality and the Nash inequality in a quantum game-theoretic setting

- Physics, EconomicsPhysics Letters A
- 2018

### Two-player quantum games: When player strategies are via directional choices

- EconomicsQuantum Inf. Process.
- 2022

We propose a scheme for a quantum game based on performing an EPR-type experiment and in which each player’s spatial directional choices are considered as their strategies. A classical mixed-strategy…

### Quantum games and games with factorizable and non-factorizable probabilities

- Physics
- 2014

A quantum game-theoretic setting enables the analysis of strategic interaction among agents with access to quantum resources. One of the original motivations for re-expressing quantum algorithms, and…

### Gaming the quantum

- PhysicsQuantum Inf. Comput.
- 2013

Finding Nash equilibrium in a strictly competitive quantum game is exhibited to be equivalent to finding a solution to a simultaneous distance minimization problem in the state space of quantum objects, thus setting up a framework for a game theory inspired study of "equilibrium" behavior of quantum physical systems such as those utilized in quantum information processing and computation.

### Quantum Coalition of “n Equipartition” Compound Mode in Minority Game

- Economics
- 2015

We investigate the quantum coalition in an N-player quantum minority game proposed by Benjamin. N players share an initial entangled state and the measure of entanglement of the initial state is p.…

### Connection between Bell nonlocality and Bayesian game theory.

- PhysicsNature communications
- 2013

There is a deep connection between Bell nonlocality and Bayesian games, and that the same concepts appear in both fields, and some of these strategies represent equilibrium points, leading to the notion of quantum/no-signalling Nash equilibrium.

### On the equivalence between non-factorizable mixed-strategy classical games and quantum games

- MathematicsRoyal Society Open Science
- 2014

It is demonstrated how the standard version of a quantum game can be analysed as a non-factorizable game and the limitations of this approach are determined.

### A new quantum game framework: When player strategies are via directional choices

- Economics
- 2021

A scheme for two-player quantum games in which each player's strategy consists of choosing the orientation of a unit vector and Nash equilibria of the game are directional pairs is presented.

### Evolution of quantum strategies on a small-world network

- Physics
- 2012

In this paper, quantum strategies are introduced within evolutionary games in order to investigate the evolution of quantum strategies on a small-world network. Initially, certain quantum strategies…

## References

SHOWING 1-10 OF 96 REFERENCES

### Analyzing Three-Player Quantum Games in an EPR Type Setup

- Physics, EconomicsPloS one
- 2011

Using GA, the formalism of Clifford Geometric Algebra is used to develop an analysis of quantum versions of three-player non-cooperative games and investigates the outcome of a realization of the game by players sharing GHZ state, W state, and a mixture of GHZ and W states.

### Analysis of Two-Player Quantum Games in an EPR Setting Using Clifford's Geometric Algebra

- PhysicsPloS one
- 2012

A general solution for two-player games is produced and the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, and hence the quantum game becomes a proper extension of the classical game, avoiding a criticism of other quantum game frameworks.

### A necessary and sufficient condition to play games in quantum mechanical settings

- Physics
- 2007

Quantum game theory is a multidisciplinary field which combines quantum mechanics with game theory by introducing non-classical resources such as entanglement, quantum operations and quantum…

### Quantum correlation games

- Physics
- 2003

A new approach to play games quantum mechanically is proposed. We consider two players who perform measurements in an EPR-type setting. The payoff relations are defined as functions of correlations,…

### Multi-Player Quantum Games

- Physics

Game theory is a mature field of applied mathematics. It formalizes the conflict between competing agents, and has found applications ranging from economics through to biology [1,2]. Quantum…

### Probabilistic analysis of three-player symmetric quantum games played using the Einstein–Podolsky–Rosen–Bohm setting

- Economics
- 2008

### Quantum game theory based on the Schmidt decomposition

- Economics
- 2007

We present a novel formulation of quantum game theory based on the Schmidt decomposition, which has the merit that the entanglement of quantum strategies is manifestly quantified. We apply this…

### Quantum strategies

- Economics
- 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.