Remarks on quantum duopoly schemes

The aim of this paper is to discuss in some detail the two different quantum schemes for duopoly problems. We investigate under what conditions one of the schemes is more reasonable than the other one. Using the Cournot’s duopoly example, we show that the current quantum schemes require a slight refinement so that they output the classical game in a particular case. Then, we show how the amendment changes the way of studying the quantum games with respect to Nash equilibria. Finally, we define another scheme for the Cournot’s duopoly in terms of quantum computation.

[1]  Yohei Sekiguchi,et al.  Uniqueness of Nash equilibria in a quantum Cournot duopoly game , 2009, 0910.5275.

[2]  L. Schiff,et al.  Quantum Mechanics, 3rd ed. , 1973 .

[3]  M. K. Khan,et al.  Quantum Stackelberg duopoly in the presence of correlated noise , 2009, 0909.0063.

[4]  J. Eisert,et al.  Quantum Games and Quantum Strategies , 1998, quant-ph/9806088.

[5]  Jiangfeng Du,et al.  The application of asymmetric entangled states in quantum games , 2005, quant-ph/0511152.

[6]  Chen Xi,et al.  Quantum Games of Continuous Distributed Incomplete Information , 2005 .

[7]  M. K. Khan,et al.  Quantum Model of Bertrand Duopoly , 2010, 1001.2831.

[8]  Hui Li,et al.  Quantum entanglement helps in improving economic efficiency , 2005 .

[9]  Hans Peters,et al.  Game Theory: A Multi-Leveled Approach , 2008 .

[10]  A. Iqbal,et al.  Backwards-induction outcome in a quantum game , 2001, quant-ph/0111090.

[11]  A. Cournot.  Researches into the Mathematical Principles of the Theory of Wealth , 1898, Forerunners of Realizable Values Accounting in Financial Reporting.

[12]  D. Meyer.  Quantum strategies , 1998, quant-ph/9804010.

[13]  L. Kuang,et al.  The influence of entanglement and decoherence on the quantum Stackelberg duopoly game , 2007 .

[14]  M. Lin,et al.  Quantum Stackelberg Duopoly of Continuous Distributed Asymmetric Information , 2007 .

[15]  M. K. Khan,et al.  Quantum Stackelberg Duopoly in a Noninertial Frame , 2011, 1102.1353.

[16]  Luca Marinatto,et al.  A quantum approach to static games of complete information , 2000 .

[17]  Hui Li,et al.  Continuous-Variable Quantum Games , 2002 .

[18]  Jiangfeng Du,et al.  Quantum games of asymmetric information. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  肖人彬,et al.  Quantum Stackelberg duopoly with isoelastic demand function , 2012 .

[20]  杜江峰,et al.  Quantum Games of Continuous Distributed Incomplete Information , 2005 .

[21]  Jiangfeng Du,et al.  Appropriate quantization of asymmetric games with continuous strategies , 2005 .

[22]  Shang-bin Li.  Simulation of continuous variable quantum games without entanglement , 2011, 1101.2388.

[23]  Ramij Rahaman,et al.  Quantum Cournot equilibrium for the Hotelling-Smithies model of product choice , 2012, ArXiv.

[24]  Xia Wang,et al.  Quantum Stackelberg Duopoly with Continuous Distributed Incomplete Information , 2012 .

[25]  D. Kiang,et al.  Quantum Bertrand duopoly with differentiated products , 2004 .

[26]  Kuang Le-Man,et al.  Quantum Stackelberg Duopoly Game in Depolarizing Channel , 2008 .

[27]  E. Merzbacher,et al.  Quantum Mechanics, 3rd Edition , 1997 .

[28]  Takashi Sato,et al.  Existence of equilibria in quantum Bertrand–Edgeworth duopoly game , 2010, Quantum Inf. Process..