# Coalitions in the quantum Minority game: Classical cheats and quantum bullies

@article{Flitney2007CoalitionsIT, title={Coalitions in the quantum Minority game: Classical cheats and quantum bullies}, author={Adrian P. Flitney and Andrew D. Greentree}, journal={Physics Letters A}, year={2007}, volume={362}, pages={132-137} }

## 11 Citations

### Strategies and payoffs in quantum minority games

- PhysicsArXiv
- 2011

This paper explores optimal and equilibrium solutions to quantum minority games, focusing on 4 and 6 player games with some N‐player generalizations.

### 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.…

### Experimental implementation of a four-player quantum game

- Physics
- 2010

Game theory is central to the understanding of competitive interactions arising in many fields, from the social and physical sciences to economics. Recently, as the definition of information is…

### 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.

### 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.

### Improving the payoffs of cooperators in three-player cooperative game using weak measurements

- EconomicsQuantum Inf. Process.
- 2015

It is shown that the payoffs of cooperators can be enhanced to a great extent in the case of amplitude damping channel, and the payoff sudden death can be avoided in the cases of bit flip and depolarizing channels.

### N-Player Quantum Games in an EPR Setting

- EconomicsPloS one
- 2012

By dispensing with the standard unitary transformations on state vectors in Hilbert space and using instead rotors and multivectors, based on Clifford’s geometric algebra, it is shown how the N-player case becomes tractable.

### Playing quantum games by a scheme with pre- and post-selection

- EconomicsQuantum Inf. Process.
- 2016

It is found that the initial state in the cooperative game does not destroy process to get preferable payoffs by pre- and post-selections, which is not true in other schemes for implementing the quantum game.

## References

SHOWING 1-10 OF 93 REFERENCES

### Multiplayer quantum Minority game with decoherence

- EconomicsSPIE International Symposium on Fluctuations and Noise
- 2005

A quantum version of the Minority game for an arbitrary number of agents is studied. When the number of agents is odd, quantizing the game produces no advantage to the players, however, for an even…

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

- PhysicsProceedings 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’…

### Quantum version of the Monty Hall problem

- Physics, Economics
- 2002

A version of the Monty Hall problem is presented where the players are permitted to select quantum strategies. If the initial state involves no entanglement the Nash equilibrium in the quantum game…

### 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,…

### Quantum and classical correlations between players in game theory

- Physics
- 2003

Effects of quantum and classical correlations on game theory are studied to clarify the new aspects brought into game theory by the quantum mechanical toolbox. In this study, we compare quantum…

### Quantum advantage does not survive in the presence of a corrupt source: optimal strategies in simultaneous move games

- Economics
- 2004

### 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.

### LETTER TO THE EDITOR: Quantum correlations and Nash equilibria of a bi-matrix game

- Economics
- 2004

Playing a symmetric bi-matrix game is usually physical implemented by sharing pairs of 'objects' between two players. A new setting is proposed that explicitly shows effects of quantum correlations…