Back
 APM  Vol.4 No.7 , July 2014
Best Response Analysis in Two Person Quantum Games
Azharuddin Shaik, Aden Ahmed*
Show more
Abstract: In this paper, we find particular use for a maximally entangled initial state that produces a quantized version of two player two strategy games. When applied to a variant of the well-known game of Chicken, our construction shows the existence of new Nash equilibria with the players receiving better payoffs than those found in literature.
Keywords: Quantum Games, Nash Equilibrium, Quaternions, Best Response Analysis, Game Extensions
Cite this paper: Shaik, A. and Ahmed, A. (2014) Best Response Analysis in Two Person Quantum Games. Advances in Pure Mathematics, 4, 341-356. doi: 10.4236/apm.2014.47045.
References

[1]   Eisert, J., Wilkens, M. and Lewenstein, M. (1999) Quantum Games and Quantum Strategies. Physical Review Letters, 83, 3077-3080. http://dx.doi.org/10.1103/PhysRevLett.83.3077

[2]   Bleiler, S.A. (2008) A Formalism for Quantum Games and an Application. Proceedings to the 9th International Pure Math Conference, Islamabad.

[3]   Nash, J. (1950) Equilibrium Points in N-Person Games. Proceedings of the National Academy of Sciences of the United States, 36, 48-49. http://dx.doi.org/10.1073/pnas.36.1.48

[4]   Landsburg, S. (2011) Nash Equilibria in Quantum Games. Proceedings of the American Mathematical Society, 139, 4423-4434. http://dx.doi.org/10.1090/S0002-9939-2011-10838-4

[5]   Ahmed, A. (2013) Quantum Games and Quaternionic Strategies. Quantum Information Processing, 12, 2701-2720.
http://dx.doi.org/10.1007/s11128-013-0553-5

[6]   Ahmed, A. (2013) Equilibria in Quantum Three-Player Dilemma Game. British Journal of Mathematics & Computer Science, 3, 195-208. http://dx.doi.org/10.1007/s11128-013-0553-5

[7]   Baez, J. (2002) The Octonions. Bulletin of the American Mathematical Society, 39, 145-205.
http://dx.doi.org/10.1090/S0273-0979-01-00934-X

[8]   Conway, J.H. and Smith, D.A. (2003) On Quaternions and Octonions. A. K. Peters, Wellesley, Massachusetts.

[9]   Ahmed, A. (2011) On Quaternions, Octonions, and the Quantization of Games: A Text on Quantum Games. Lambert Academic Publishing, Saarbrücken.

[10]   Ahmed, A.O., Bleiler, S.A. and Khan, F.S. (2010) Octonionization of Three-Player, Two-Strategy Maximally Entangled Quantum Games. International Journal of Quantum Information, 8, 411-434.
http://dx.doi.org/10.1142/S0219749910006344

 
 
Top