Best Response Analysis in Two Person Quantum Games


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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Eisert, J., Wilkens, M. and Lewenstein, M. (1999) Quantum Games and Quantum Strategies. Physical Review Letters, 83, 3077-3080.
[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.
[4] Landsburg, S. (2011) Nash Equilibria in Quantum Games. Proceedings of the American Mathematical Society, 139, 4423-4434.
[5] Ahmed, A. (2013) Quantum Games and Quaternionic Strategies. Quantum Information Processing, 12, 2701-2720.
[6] Ahmed, A. (2013) Equilibria in Quantum Three-Player Dilemma Game. British Journal of Mathematics & Computer Science, 3, 195-208.
[7] Baez, J. (2002) The Octonions. Bulletin of the American Mathematical Society, 39, 145-205.
[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.

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