Existence of equilibria in quantum Bertrand–Edgeworth duopoly game

Both classical and quantum version of two models of price competition in duopoly market, the one is realistic and the other is idealized, are investigated. The pure strategy Nash equilibria of the realistic model exists under stricter condition than that of the idealized one in the classical form game. This is the problem known as Edgeworth paradox in economics. In the quantum form game, however, the former converges to the latter as the measure of entanglement goes to infinity.

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

[2]  D. E. Matthews.  Evolution and the Theory of Games , 1977 .

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

[4]  Jiangfeng Du,et al.  Quantum Bertrand duopoly of incomplete information , 2005 .

[5]  Simon C. Benjamin,et al.  Multiplayer quantum games , 2001 .

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

[7]  D. Kiang,et al.  Quantum Stackelberg duopoly , 2003 .

[8]  Philip V. Fellman.  The Nash Equilibrium Revisited: Chaos and Complexity Hidden in Simplicity , 2007, ArXiv.

[9]  W. Hamilton,et al.  The Evolution of Cooperation , 1984 .

[10]  R. Gibbons.  Game theory for applied economists , 1992 .

[11]  A. H. Toor,et al.  Stability of Mixed Nash Equilibria in Symmetric Quantum Games , 2001 .

[12]  Hui Li,et al.  Quantum Strategy Without Entanglement , 2000, quant-ph/0011078.

[13]  J. Tirole.  The Theory of Industrial Organization , 1988 .

[14]  Azhar Iqbal,et al.  Quantum mechanics gives stability to a Nash equilibrium , 2002 .

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

[16]  J. Bertrand.  Cournot oligopoly: Review of Walras's Théorie mathématique de la richesse sociale and Cournot's Recherches sur les principes mathématiques de la théorie des richesses , 1989 .

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

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

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

[20]  J M Smith,et al.  Evolution and the theory of games , 1976 .

[21]  Azhar Iqbal,et al.  Playing games with EPR-type experiments , 2005, quant-ph/0507152.

[22]  Neil Johnson,et al.  Efficiency and formalism of quantum games , 2003 .

[23]  D. Kiang,et al.  Quantum Stackelberg duopoly with incomplete information , 2005 .

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

[25]  E. Maskin,et al.  The Existence of Equilibrium in Discontinuous Economic Games, II: Applications , 1986 .

[26]  J. Nash.  Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.