International Journal of Theoretical Physics

, Volume 42, Issue 5, pp 1089–1099 | Cite as

An Invitation to Quantum Game Theory

  • E. W. Piotrowski
  • J. Sładkowski
Article

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.

quantum games quantum strategies econophysics financial markets Ising model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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.Google Scholar
  2. D'Ariano, G. M. et al. (2002). The quantum Monty Hall problem. Quantum Information and Computing 2, 355.Google Scholar
  3. Du, J. et al. (2001). Remarks on quantum battle of sexes game. Preprint quant-ph/0103004.Google Scholar
  4. Du, J. et al. (2002). Experimental realization of quantum games on a quantum computer Physical Review Letters 88, 137902.Google Scholar
  5. Eisert, J., Wilkens, M., and Lewenstein, M. (1999). Quantum games and quantum strategies. Physical Review Letters 83, 3077.Google Scholar
  6. Ekert, A. (1991). Quantum cryptography based on Bell's theorem. Physical Review Letters 67, 661.Google Scholar
  7. Feynmann, R. P. (1972). Statistical Physics. A Set of Lectures, Benjamin Inc., Menlo Park.Google Scholar
  8. Flitney, A. P. and Abbott, D. (2002). Quantum version of the Monty Hall problem. Physical Review A 65, 062318.Google Scholar
  9. Flitney, A. P., Ng, J., and Abbott, D. (2002). Quantum Parrondo's games. Physica A 314, 384.Google Scholar
  10. 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.Google Scholar
  11. Gillman, L. (1992). The car and the goats. American Mathematical Monthly 99, 3.Google Scholar
  12. Goldenberg, L., Vaidman, L., and Wiesner, S. (1999). Quantum gambling. Physical Review Letters 82, 3356.Google Scholar
  13. Grib, A. and Parfionov, G. (2002a). Can the game be quantum? Preprint quant-ph/0206178.Google Scholar
  14. Grib, A. and Parfionov, G. (2002b). Macroscopic quantum game. Preprint quant-ph/0211068.Google Scholar
  15. Harmer, G. P. and Abbott, D. (1999). Parrondo's paradox. Statistical Science 14, 206.Google Scholar
  16. Hwang, W. Y., Ahn, D., and Hwang, S. W. (2001). Quantum gambling using two nonorthogonal states. Physical Review A 64, 064302.Google Scholar
  17. Iqbal, A. and Toor, A. H. (2001). Evolutionary stable strategies in quantum games. Physics Letters A 280, 249.Google Scholar
  18. Meyer, D. (1999). Quantum strategies. Physical Review Letters 82, 1052.Google Scholar
  19. 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.Google Scholar
  20. Osborne, M. J. (1994). A Course in Game Theory, MIT Press, Boston.Google Scholar
  21. Pietarinen, A. (2002). Quantum logic and quantum theory in a game-theoretic perspective. Open Systems and Information Dynamics 9, 273.Google Scholar
  22. Piotrowski, E. W. and Sladkowski, J. (2001a). The thermodynamics of portfolios. Acta Physica Polonica B 32, 597.Google Scholar
  23. Piotrowski, E. W. and Sladkowski, J. (2001b). Quantum-like approach to financial risk: Quantum anthropic principle. Acta Physica Polonica B 32, 3873.Google Scholar
  24. Piotrowski, E. W. and Sladkowski, J. (2002a). Quantum solution to the Newcomb's paradox. Preprint quant-ph/0202074.Google Scholar
  25. Piotrowski, E. W. and Sładkowski, J. (2002b). Quantum bargaining games. Physica A 308, 391.Google Scholar
  26. Piotrowski, E. W. and Sładkowski, J. (2002c). Quantum market games. Physica A 312, 208.Google Scholar
  27. Piotrowski, E. W. and Sładkowski, J. (in press). Quantum English auctions. Physica A.Google Scholar
  28. Pitowsky, I. (2002). Betting on the outcomes of measurements: A Bayesian theory of quantum probability. Preprint quant-ph/0208121.Google Scholar
  29. 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.Google Scholar
  30. 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.Google Scholar
  31. Straffin, P. D. (1993). Game Theory and Strategy. AMS, Rhode Island.Google Scholar
  32. 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.Google Scholar
  33. von Neumann, J. and Morgenstern, O. (1953). Theory of Games and Economic Behavior, Princeton University Press, Princeton.Google Scholar
  34. Waite, S. (2002). Quantum Investing, Texere Publishing, London.Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • E. W. Piotrowski
    • 1
  • J. Sładkowski
    • 2
  1. 1.Institute of Theoretical PhysicsUniversity of BiałystokPoland
  2. 2.Institute of PhysicsUniversity of SilesiaKatowicePoland

Personalised recommendations