Best Response Analysis in Two Person Quantum Games
Affiliation(s)
Department of Mathematics, Texas A & M University—Kingsville, Kingsville, Texas, USA.
Department of Mathematics, Texas A & M University—Kingsville, Kingsville, Texas, USA.
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.
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.
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
[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