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Quantum Model of Bertrand Duopoly |
| Salman Khan, M. Ramzan, M. K. Khan |
| Department of Physics Quaid-i-Azam University, Islamabad 45320, Pakistan |
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| Cite this article: |
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Salman Khan, M. Ramzan, M. K. Khan 2010 Chin. Phys. Lett. 27 080302 |
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Abstract We present a quantum model of Bertrand duopoly and study the entanglement behavior on the profit functions of the firms. Using the concept of optimal response of each firm to the price of the opponent, we find only one Nash equilibirum point for the maximally entangled initial state. The presence of quantum entanglement in the initial state gives payoffs higher to the firms than the classical payoffs at the Nash equilibrium. As a result, the dilemma-like situation in the classical game is resolved.
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| Keywords:
03.65.Ta
03.65.-w
03.67.Lx
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Received: 26 January 2010
Published: 28 July 2010
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| PACS: |
03.65.Ta
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(Foundations of quantum mechanics; measurement theory)
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03.65.-w
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(Quantum mechanics)
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03.67.Lx
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(Quantum computation architectures and implementations)
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[1] Gibbons R 1992 Game Theory for Applied Economists (Princeton, NJ: Princeton University Press)
Bierman H S, Fernandez L 1998 Game Theory with Economic Applications 2nd edn (Reading MA: Addison-Wesley)
[2] Cournot A 1897 Researches into the Mathematical Principles of the Theory of Wealth (New York: Macmillan)
[3] Bertrand J and Savants J 1883 Journal des Savants 67 499
[4] Stackelberg H von 1934 Marktform und Gleichgewicht (Vienna: Springer)
[5] Flitney A P, Ng J and Abbott D 2002 Physica A 314 35
[6] Ramzan M et al 2008 J. Phys. A: Math. Theor. 41 055307
[7] D' Ariano G M 2002 Quantum Information and Computation 2 355
[8] Flitney A P and Abbott D 2002 Phys. Rev. A 65 062318
[9] Iqbal A, Cheo T and Abbott D 2008 Phys. Lett. A 372 6564
[10] Zhu X and Kaung L M 2008 Commun. Theor. Phys. 49 111
[11] Ramzan M and Khan M K 2008 J. Phys. A: Math. Theor. 41 435302
[12] Ramzan M and Khan M K 2009 J. Phys. A: Math. Theor. 42 025301
[13] Zhu X and Kaung L M 2007 J. Phys. A 40 7729
[14] Salman Khan et al 2010 Int. J. Theor. Phys. 49 31
[15] Meyer D A 1999 Phys. Rev. Lett. 82 1052
[16] Eisert J et al 1999 Phys. Rev. Lett. 83 3077
[17] Marinatto L and Weber T 2000 Phys. Lett. A 272 291
[18] Li H, Du J and Massar S 2002 Phys. Lett. A 306 73
[19] Lo C F and Kiang D 2004 Phys. Lett. A 321 94
[20] Iqbal A and Abbott D 2009 arXiv:quant-ph/0909.3369
[21] Iqbal A and Toor A H 2002 Phys. Rev. A 65 052328
[22] Lo C F and Kiang D 2003 Phys. Lett. 318 333
[23] Benjamin S C and Hayden P M 2001 Phys. Rev. A 64 030301
[24] Lo C F and Kiang D 2005 Phys. Lett. A 346 65
[25] Qin G et al 2005 J. Phys. A: Math. Gen. 38 4247
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