Quantum logics, games, and equilibriums
Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 2, pp. 259-271 Cet article a éte moissonné depuis la source Math-Net.Ru

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We establish a natural relation between antagonistic matrix games and ortholattices (quantum logics). We show that an equilibrium in the corresponding quantum game determines the operator representation of a quantum logic. We formulate a condition for quantum equilibrium.
Keywords: quantum logic, lattice, quantum game, Nash equilibrium.
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A. A. Grib; G. N. Parfionov. Quantum logics, games, and equilibriums. Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 2, pp. 259-271. http://geodesic.mathdoc.fr/item/TMF_2011_169_2_a7/

[1] A. A. Grib, G. N. Parfionov, J. Math. Sci., 125:2 (2005), 173–184 | DOI | MR

[2] L. K. Franeva, A. A. Grib, G. N. Parfionov, “Quantum games of macroscopic partners”, Proc. I Internat. Conf. “Game Theory and Management” (St. Petersburg, Russia, June 28–29, 2007), Grad. Sch. Manag., St. Petersb. Univ., St. Petersburg, 2008, 130–152 {http://www.gsom.pu.ru/en/research/conferences/}

[3] A. A. Grib, G. N. Parfionov, “How to play macroscopic quantum game”, Proc. II Internat. Conf. “Game Theory and Management” (St. Petersburg, Russia, June 26–27, 2008), Grad. Sch. Manag., St. Petersb. Univ., St. Petersburg, 2009, 137–146 {http://www.gsom.pu.ru/en/research/conferences/} | MR | Zbl

[4] A. A. Grib, G. N. Parfionov, “Quantum Nash-equilibrium and linear representations of ortholattices”, Proc. III Internat. Conf. “Game Theory and Management” (St. Petersburg, Russia, June 24–26, 2009), Grad. Sch. Manag., St. Petersb. Univ., St. Petersburg, 2010, 132–143 {http://www.gsom.pu.ru/en/research/conferences/} | MR | Zbl

[5] D. A. Meyer, Phys. Rev. Lett., 82:5 (1999), 1052–1055, arXiv: quant-ph/9804010 | DOI | MR | Zbl

[6] J. Eisert, M. Wilkens, M. Lewenstein, Phys. Rev. Lett., 83:15 (1999), 3077–3080, arXiv: quant-ph/9806088 | DOI | MR | Zbl

[7] L. Marinatto, T. Weber, Phys. Lett. A, 272:5–6 (2000), 291–303, arXiv: quant-ph/0004081 | DOI | MR | Zbl

[8] G. Parfionov, Multiple Nash-equilibrium in quantum game, arXiv: 0806.1102