Journal of Mathematical Sciences

, Volume 125, Issue 2, pp 173–184

Can a Game be Quantum?

  • A. A. Grib
  • G. N. Parfionov

DOI: 10.1023/B:JOTH.0000049569.80798.b0

Cite this article as:
Grib, A.A. & Parfionov, G.N. Journal of Mathematical Sciences (2005) 125: 173. doi:10.1023/B:JOTH.0000049569.80798.b0


A game in which acts of the participants do not have an adequate description in terms of the Boolean logic and classical theory of probabilities is considered. A model of the game interaction is constructed on the basis of a nondistributive orthocomplemented lattice. Mixed strategies of the participants are calculated using probability amplitudes according to the rules of quantum mechanics. A scheme of quantization of the payoff function is proposed and an algorithm for the search of the Nash equilibrium is given. It is shown that in contrast with the classical case, in the quantum situation a discrete set of equilibria is possible. Bibliography: 19 titles.

Copyright information

© Plenum Publishing Corporation 2005

Authors and Affiliations

  • A. A. Grib
    • 1
  • G. N. Parfionov
    • 2
  1. 1.Friedman Laboratory of Theoretical PhysicsU.S.A
  2. 2.St.Petersburg University for Economics and FinancesU.S.A

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