Transitivity of an entangled choice

We describe a quantum model of a simple choice game (constructed upon the entangled state of two qubits), which involves the fundamental problem of transitive–intransitive preferences. We compare attainability of optimal intransitive strategies in both classical and quantum models with the use of geometrical interpretation.

[1]  A. Pechenkin.  B P Belousov and his reaction , 2009, Journal of Biosciences.

[2]  Edward W. Piotrowski,et al.  An Invitation to Quantum Game Theory , 2002, ArXiv.

[3]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[4]  L. A. Goodman,et al.  Social Choice and Individual Values , 1951 .

[5]  P. Fishburn.  Nontransitive preferences in decision theory , 1991 .

[6]  Katarzyna Miakisz,et al.  Quantization of games: Towards quantum artificial intelligence , 2006, Theor. Comput. Sci..

[7]  Edward W. Piotrowski,et al.  Universality of measurements on quantum markets , 2005 .

[8]  Derek Abbott,et al.  AN INTRODUCTION TO QUANTUM GAME THEORY , 2002 .

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

[10]  P. Anand,et al.  Foundations of Rational Choice Under Risk. , 1993 .

[11]  E. W. Piotrowski,et al.  Quantum Market Games , 2001 .

[12]  Stephen Wiesner,et al.  Conjugate coding , 1983, SIGA.

[13]  Gordon Tullock,et al.  THE IRRATIONALITY OF INTRANSITIVITY , 1964 .

[14]  J. Marschak,et al.  Oxford Economic Papers. , 1939 .

[15]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[16]  Relative entropy, Haar measures and relativistic canonical velocity distributions , 2006, cond-mat/0610045.

[17]  M. K. Khan,et al.  Noisy non-transitive quantum games , 2009, 0912.4961.

[18]  Edward W. Piotrowski,et al.  Quantum cat's dilemma: an example of intransitivity in a quantum game , 2006 .

[19]  L. Vaidman.  Variations on the Theme of the Greenberger-Horne-Zeilinger Proof , 1998 .

[20]  Marcin Makowski,et al.  Transitivity vs. intransitivity in decision making process – an example in quantum game theory , 2009, 0901.1603.

[21]  Peter Baumann.  Theory Choice and the Intransitivity of ‘Is a Better Theory Than’* , 2005, Philosophy of Science.

[22]  S. Shafir.  Intransitivity of preferences in honey bees: support for 'comparative' evaluation of foraging options , 1994, Animal Behaviour.

[23]  L. Boddy,et al.  Interspecific combative interactions between wood-decaying basidiomycetes. , 2000, FEMS microbiology ecology.

[24]  Logan Grosenick,et al.  Fish can infer social rank by observation alone , 2007, Nature.

[25]  Edward W. Piotrowski,et al.  CAT'S DILEMMA — TRANSITIVITY VS. INTRANSITIVITY , 2004 .