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2014 | 178 | 174-189

Article title

Dlaczego w dylemat więźnia warto grać kwantowo?



Title variants

Why is it Worth Playing Quantum Prisoner's Dilemma?

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The Prisoner's Dilemma [PD] is the best known example of a two-person, simultaneous game, for which the Nash equilibrium is far from Pareto-optimal solutions. In this paper we define a quantum PD, for which player's strategies are defined as rotations of the SU(2) group, parameterized by three angles. Quantum strategies are correlated through the mechanism of quantum entanglement and the result of the game is obtained by the collapse of the wave function. Classic PD is a particular case of the quantum game for which the set of rotations is limited to one dimension. Each quantum strategy can be, by appropriate choice of counter-strategy, interpreted as a "cooperation" or "defection". Quantum PD has Nash equilibria that are more favorable than the classic PD and close to the Pareto optimal solutions. With proper selection of strategies, quantum PD can be reduced to the classic, zero-sum, "matching pennies" game. In this paper we show examples of economic phenomena (price collusion, the chess strategy) that mimics the Nash equilibria of quantum PD.








Physical description




  • Albrecht A., Phillips D., 2012: Origin of Probabilities and Their Application to the Multiverse [Online]. Cornell University Library, http://arxiv.org/pdf/1212.0953 v1.pdf [dostęp: 12.2012].
  • Busemeyer J.R., Wang Z., Townsend J.T., 2006: Quantum Dynamics of Human Decision Making. "Journal of Mathematical Psychology", Vol. 50, 220-241.
  • Chen K., Hogg T., 2006: How Well Do People Play a Quantum Prisoner's Dilemma. "Quantum Information Processing", Vol. 5(1), 43-67.
  • Cialdini R., 1995: Wywieranie wpływu na ludzi. Gdańskie Wydawnictwo Psychologiczne, Gdańsk.
  • Dixit A.K., Nalebuff B.J., 2009: Sztuka strategii. MT Biznes, Warszawa.
  • Du J. et al., 2002: Experimental Realization of Quantum Games on Quantum Computer. "Physical Review Letters", Vol. 88, 137902.
  • Eisert J., Wilkens M., Lewenstein M., 1999: Quantum Games and Quantum Strategies. "Physical Review Letters", Vol. 83, 3077, s. 3077.
  • Flitney A.P., Abbott D., 2002: An Introduction to Quantum Game Theory. "Fluct. Noise Lett", Vol. 2, R175-87.
  • Flood M.M., Dresher M., 1952: Research Memorandum. RM-789-1-PR. RAND Corporation, Santa-Monica, Ca.
  • Goldenberg L., Vaidman L., Wiesner S., 1999: Quantum Gambling. "Physical Review Letters", Vol. 82, 3356.
  • Hamilton W.D., Axelrod R., 1981: The Evolution of Cooperation. "Science", Vol. 211.27, 1390-1396.
  • Perrotin R., Heusschen P., 1994: Kupić z zyskiem. Poltext, Warszawa.
  • Piotrowski E., Sładkowski J., 2008: Quantum Auctions: Facts and Myths. "Physica A", 15, Vol. 387, 3949-3953.
  • -, 2002: Quantum Market Games. "Physica A", 1-2, Vol. 312, 208-216.
  • Pothos E.M., Busemeyer J.R., 2009: A Quantum Probability Explanation for Violations of 'Rational' Decision Theory. Proceedings of the Royal Society B., Vol. 276, 2171-2178.
  • Straffin P.D., 2001: Teoria gier. WN Scholar, Warszawa.
  • Szopa M., 2010: Teoria gier w negocjacjach. Skrypty dla studentów Ekonofizyki na Uniwersytecie Śląskim [Online]. http://el.us.edu.pl/ekonofizyka/index.php/ Teoria_gier/strategie_taktyki_negocjacji.
  • Vandersypen L.M.K. et al., 2001: Experimental Realization of Shor's Quantum Factoring Algorithm Using Nuclear Magnetic Resonance. "Nature", 6866, Vol. 414, 883-887.

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