The relationship between quantum and classical correlation in games

Quantum games have been argued to differ from classical games by virtue of the quantum-mechanical phenomenon of entanglement. We formulate a baseline of classical correlation - which takes two forms according as signals added to the game are or are not required to be independent of chance moves in the underlying game. We show that independence is a necessary condition for the addition of quantum signals to have a different effect from the addition of classical signals.

[1]  Shmuel Zamir,et al.  Type Indeterminacy: A Model for the KT(Kahneman-Tversky)-Man , 2006, physics/0604166.

[2]  Vladislav Kargin,et al.  On coordination games with quantum correlations , 2008, Int. J. Game Theory.

[3]  M. Rédei.  Letter to E. Schrödinger , 2005 .

[4]  E. Schrödinger.  Discussion of Probability Relations between Separated Systems , 1935, Mathematical Proceedings of the Cambridge Philosophical Society.

[5]  Simon C. Benjamin,et al.  Multiplayer quantum games , 2001 .

[6]  J. Neumann.  Mathematische grundlagen der Quantenmechanik , 1935 .

[7]  R. Aumann.  Correlated Equilibrium as an Expression of Bayesian Rationality Author ( s ) , 1987 .

[8]  van Enk.  Quantum and classical game strategies , 2000 .

[9]  C. Lance.  John von Neumann: Selected letters (History of Mathematics 27) , 2008 .

[10]  F. Laloë,et al.  Do we really understand quantum mechanics? Strange correlations, paradoxes, and theorems , 2001, quant-ph/0209123.

[11]  Peter Høyer,et al.  Consequences and limits of nonlocal strategies , 2004, Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004..

[12]  Adam Brandenburger,et al.  Intrinsic correlation in games , 2008, J. Econ. Theory.

[13]  Adam Brandenburger,et al.  A classification of hidden-variable properties , 2007, 0711.4650.

[14]  J. Eisert,et al.  Quantum Games and Quantum Strategies , 1998, quant-ph/9806088.

[15]  W. Michael Dickson.  Quantum chance and non-locality: Probability and non-locality , 1998 .

[16]  D. Meyer.  Quantum strategies , 1998, quant-ph/9804010.

[17]  James E. Jarrett,et al.  On the Physical Significance of the Locality Conditions in the Bell Arguments , 1984 .

[18]  Pierfrancesco La Mura.  Correlated Equilibria of Classical Strategic Games with Quantum Signals , 2003, ArXiv.

[19]  R. Penrose,et al.  Quantum Concepts in Space and Time , 1986 .

[20]  J. Bell.  On the Problem of Hidden Variables in Quantum Mechanics , 1966 .

[21]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[22]  Stefan Weigert,et al.  Quantum correlation games , 2003 .

[23]  Abner Shimony,et al.  Search for a naturalistic world view: Events and processes in the quantum world , 1993 .

[24]  Miklós Rédei.  John von Neumann - selected letters , 2006, History of mathematics.

[25]  E. Rowland.  Theory of Games and Economic Behavior , 1946, Nature.

[26]  J. Neumann.  Zur Theorie der Gesellschaftsspiele , 1928 .

[27]  Jens Eisert,et al.  Quantum games , 2000 .

[28]  R. Aumann.  Subjectivity and Correlation in Randomized Strategies , 1974 .

[29]  D. E. Smith,et al.  History of Mathematics , 1924, Nature.

[30]  L. Hardy,et al.  Nonlocality for two particles without inequalities for almost all entangled states. , 1993, Physical review letters.

[31]  J. J. Sakurai,et al.  Modern Quantum Mechanics , 1986 .

[32]  Tad Hogg,et al.  Quantum Solution of Coordination Problems , 2003, Quantum Inf. Process..

[33]  S. J. van Enk,et al.  Classical rules in quantum games , 2002 .

[34]  L. Hardy,et al.  Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories. , 1992, Physical review letters.

[35]  Ted Temzelides.  An Uncertainty Principle for Social Science Experiments , 2006 .

[36]  David K. Levine,et al.  Quantum Games Have No News For Economics , 2005 .

[37]  J. J. Sakurai,et al.  Modern Quantum Mechanics, Revised Edition , 1995 .

[38]  Steven E. Landsburg,et al.  Nash equilibria in quantum games , 2011, 1110.1351.

[39]  E. Specker,et al.  The Problem of Hidden Variables in Quantum Mechanics , 1967 .