Abstract
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history, basic ideas, and recent development in quantum game theory. In this context, a new application of the Ising chain model is proposed.
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Bennett, C. H. and Brassard, G. (1984). Quantum cryptography: Public-key distribution and coin tossing. In Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, December 1984, IEEE, New York, p. 175.
D'Ariano, G. M. et al. (2002). The quantum Monty Hall problem. Quantum Information and Computing 2, 355.
Du, J. et al. (2001). Remarks on quantum battle of sexes game. Preprint quant-ph/0103004.
Du, J. et al. (2002). Experimental realization of quantum games on a quantum computer Physical Review Letters 88, 137902.
Eisert, J., Wilkens, M., and Lewenstein, M. (1999). Quantum games and quantum strategies. Physical Review Letters 83, 3077.
Ekert, A. (1991). Quantum cryptography based on Bell's theorem. Physical Review Letters 67, 661.
Feynmann, R. P. (1972). Statistical Physics. A Set of Lectures, Benjamin Inc., Menlo Park.
Flitney, A. P. and Abbott, D. (2002). Quantum version of the Monty Hall problem. Physical Review A 65, 062318.
Flitney, A. P., Ng, J., and Abbott, D. (2002). Quantum Parrondo's games. Physica A 314, 384.
Gaubert, S. and Plus, M. (1997). Methods and applications of max-plus linear algebra. In Lecture Notes in Computer Sciences, Vol. 1200, Springer, New York.
Gillman, L. (1992). The car and the goats. American Mathematical Monthly 99, 3.
Goldenberg, L., Vaidman, L., and Wiesner, S. (1999). Quantum gambling. Physical Review Letters 82, 3356.
Grib, A. and Parfionov, G. (2002a). Can the game be quantum? Preprint quant-ph/0206178.
Grib, A. and Parfionov, G. (2002b). Macroscopic quantum game. Preprint quant-ph/0211068.
Harmer, G. P. and Abbott, D. (1999). Parrondo's paradox. Statistical Science 14, 206.
Hwang, W. Y., Ahn, D., and Hwang, S. W. (2001). Quantum gambling using two nonorthogonal states. Physical Review A 64, 064302.
Iqbal, A. and Toor, A. H. (2001). Evolutionary stable strategies in quantum games. Physics Letters A 280, 249.
Meyer, D. (1999). Quantum strategies. Physical Review Letters 82, 1052.
Milnor, J. (1954). Games against nature. In Decision Processes, R. M. Thrall, C. H. Coombs, and R. L. Davis, eds., Wiley, New York, p. 49.
Osborne, M. J. (1994). A Course in Game Theory, MIT Press, Boston.
Pietarinen, A. (2002). Quantum logic and quantum theory in a game-theoretic perspective. Open Systems and Information Dynamics 9, 273.
Piotrowski, E. W. and Sladkowski, J. (2001a). The thermodynamics of portfolios. Acta Physica Polonica B 32, 597.
Piotrowski, E. W. and Sladkowski, J. (2001b). Quantum-like approach to financial risk: Quantum anthropic principle. Acta Physica Polonica B 32, 3873.
Piotrowski, E. W. and Sladkowski, J. (2002a). Quantum solution to the Newcomb's paradox. Preprint quant-ph/0202074.
Piotrowski, E. W. and Sładkowski, J. (2002b). Quantum bargaining games. Physica A 308, 391.
Piotrowski, E. W. and Sładkowski, J. (2002c). Quantum market games. Physica A 312, 208.
Piotrowski, E. W. and Sładkowski, J. (in press). Quantum English auctions. Physica A.
Pitowsky, I. (2002). Betting on the outcomes of measurements: A Bayesian theory of quantum probability. Preprint quant-ph/0208121.
Shor, P. W. (1994). Algorithms for quantum computation: Discrete logarithms and factoring. In Proceedings of the 35th Symposium on Foundations of Computer Science, Santa Fe, S. Goldwasser, ed., IEEE Computer Society Press, Los Alamitos, p. 124.
Simon, D. R. (1994). On the power of quantum computation. In Proceedings of the 35th Symposium on Foundations of Computer Science, Santa Fe, S. Goldwasser, ed., IEEE Computer Society Press, Los Alamitos, p. 116.
Straffin, P. D. (1993). Game Theory and Strategy. AMS, Rhode Island.
Vandersypen, L. M. K., Steffen, M., Breyta, G., Yannoni, C. S., and Chuang, I. L. (2001). Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883.
von Neumann, J. and Morgenstern, O. (1953). Theory of Games and Economic Behavior, Princeton University Press, Princeton.
Waite, S. (2002). Quantum Investing, Texere Publishing, London.
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Piotrowski, E.W., Sładkowski, J. An Invitation to Quantum Game Theory. International Journal of Theoretical Physics 42, 1089–1099 (2003). https://doi.org/10.1023/A:1025443111388
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DOI: https://doi.org/10.1023/A:1025443111388