Quantum game theory

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Quantum game theory is an extension of classical game theory to scenarios that contain quantum effects . It differs from classical game theory mainly in terms of the possibilities of using superimposed initial states or entangled initial states or of using superimposed strategies. In multiplayer games, quantum correlations do not allow possible forms of cooperation in traditional game theory. Quantum game theory can be seen as part of quantum informatics . The first work on quantum game theory was published in 1999. Games for which quantum versions have been studied include the Prisoner's Dilemma , the Mean King's Problem, and the Goat Problem .

Quantum mechanics can find its way into the game situation in various ways: The game pieces or coins can be understood as a quantum system, which allows new moves (for example, those that bring the game to superimposed states). In addition, the possibility of quantum communication between the participants or the use of entangled states (with whose quantum correlations the other players can coordinate their actions) enable new strategies. In both zero-sum games and non-zero-sum games, this can lead to new optimal solutions and equilibrium solutions that do not traditionally exist. For example, entanglement can be used to prevent gamblers from taking advantage of cheating.

literature

  • Hong Guo, Juheng Zhang, Gary J. Koehler: A survey of quantum games . In: Decision Support Systems . tape 46 , no. 1 , December 2008, p. 318–332 , doi : 10.1016 / j.dss.2008.07.001 (English).
  • Julia Kempe, Hirotada Kobayashi, Keiji Matsumoto, Ben Toner, Thomas Vidick: Entangled Games Are Hard to Approximate . In: SIAM J. Comput. tape 40 , no. 3 , p. 848-877 , doi : 10.1137 / 090751293 , arxiv : 0704.2903 .
  • Tom Cooney, Marius Junge, Carlos Palazuelos, David Pérez-García: Rank-one Quantum Games . In: Computational Complexity . tape 24 , no. 1 . Springer, Basel March 1, 2015, p. 133-196 , arxiv : 1112.3563 .
  • Edward W. Piotrowski, Jan Sładkowski: Quantum Game Theoretical Frameworks in Economics . In: E. Haven, A. Khrennikov (Eds.): The Palgrave Handbook of Quantum Models in Social Science . Palgrave, London 2017, pp. 39–57 , doi : 10.1057 / 978-1-137-49276-0_3 (English, springer.com [PDF]).

Individual evidence

  1. ^ A b David A. Meyer: Quantum strategies . In: Phys. Rev. Lett. tape 82 , February 1, 1999, p. 1052-1055 , doi : 10.1103 / PhysRevLett.82.1052 , arxiv : quant-ph / 9804010 .
  2. ^ A b c Jens Eisert, Martin Wilkens, Maciej Lewenstein : Quantum Games and Quantum Strategies . In: Phys. Rev. Lett. tape 83 , October 11, 1999, pp. 3077-3080 , doi : 10.1103 / PhysRevLett.83.3077 , arxiv : quant-ph / 9806088 .
  3. ↑ Ramón Alonso-Sanz: A quantum prisoner's dilemma cellular automaton . In: Proceedings of the Royal Society A . tape 470 , no. 2146 , February 14, 2014, p. 2013079 , doi : 10.1098 / rspa.2013.0793 .
  4. ^ Berthold-Georg Englert, Yakir Aharonov : The mean king's problem: prime degrees of freedom . In: Physics Letters A . tape 284 , no. 1 , May 28, 2001, p. 1-5 , arxiv : quant-ph / 0101134 .
  5. ↑ GM D'Ariano, RD Gill, M. Keyl, B. Kümmerer, H. Maassen, RF Werner : The Quantum Monty Hall Problem . In: Quant. Inf. Comput. tape 2 , no. 5 , 2002, p. 355-366 , arxiv : quant-ph / 0202120 .
  6. ↑ Simon C. Benjamin, Patrick M. Hayden: Multiplayer quantum games . In: Phys. Rev. A . tape 64 , no. 3 , August 13, 2001, p. 030301 , doi : 10.1103 / PhysRevA.64.030301 , arxiv : quant-ph / 0007038 .