General Model for an Entanglement-Enhanced Composed Quantum Game on a Two-Dimensional Lattice

We introduce a method of analyzing entanglement-enhanced quantum games on regular lattices of agents. Our method is valid for setups with periodic and non-periodic boundary conditions. To demonstrate our approach we study two different types games, namely the Prisoner's dilemma game and a cooperative Parrondo's game. In both cases we obtain results showing, that entanglement is a crucial resource necessary for the agents to achieve positive capital gain.

[1]  D. Abbott,et al.  Quantum Parrondo's games , 2002 .

[2]  Philip Mirowski,et al.  More Heat Than Light: Economics as Social Physics , 1989 .

[3]  Philip Mirowski,et al.  More Heat than Light , 1989 .

[4]  S. Galam.  Sociophysics: A Physicist's Modeling of Psycho-political Phenomena , 2012 .

[5]  J. Sladkowski.  Giffen paradoxes in quantum market games , 2002 .

[6]  M. Nowak,et al.  Evolutionary games and spatial chaos , 1992, Nature.

[7]  D. Abbott,et al.  Quantum walks with history dependence , 2003, quant-ph/0311009.

[8]  Piotr Gawron,et al.  Quantum Implementation of Parrondo's Paradox , 2005, ArXiv.

[9]  Andrei Khrennikov,et al.  Ubiquitous Quantum Structure , 2010 .

[10]  C. M. Chandrashekar,et al.  Parrondoʼs game using a discrete-time quantum walk , 2010, 1008.5121.

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

[12]  M. Tomassini,et al.  Social Dilemmas and Cooperation in Complex Networks , 2006 .

[13]  Derek Abbott,et al.  Parrondo's paradox , 1999 .

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

[15]  W. Hamilton,et al.  The Evolution of Cooperation , 1984 .

[16]  Rosario N. Mantegna,et al.  An Introduction to Econophysics: Contents , 1999 .

[17]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[18]  Jan Sladkowski,et al.  Cooperative quantum Parrondo’s games , 2012, 1207.6954.

[19]  Rosario N. Mantegna,et al.  Book Review: An Introduction to Econophysics, Correlations, and Complexity in Finance, N. Rosario, H. Mantegna, and H. E. Stanley, Cambridge University Press, Cambridge, 2000. , 2000 .

[20]  Piotr Gawron,et al.  Qubit flip game on a Heisenberg spin chain , 2011, Quantum Inf. Process..

[21]  D. Saklofske,et al.  Personality and Individual Differences , 2018, Rethinking Georg Simmel's Social Philosophy.

[22]  R. Toral.  Cooperative Parrondo's Games , 2001 .

[23]  Derek Abbott,et al.  Quantum Strategies Win in a Defector-Dominated Population , 2011, ArXiv.

[24]  James T. Townsend,et al.  Quantum dynamics of human decision-making , 2006 .

[25]  Andrei Khrennikov,et al.  Ubiquitous Quantum Structure: From Psychology to Finance , 2010 .

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

[27]  Hendrik B. Geyer,et al.  Journal of Physics A - Mathematical and General, Special Issue. SI Aug 11 2006 ?? Preface , 2006 .

[28]  Adrian P. Flitney,et al.  Nash equilibria in quantum games with generalized two-parameter strategies , 2007 .

[29]  Philip Mirowski,et al.  More Heat Than Light: Economics as Social Physics , 1989 .

[30]  J. Busemeyer,et al.  Understanding cooperation in the Prisoner’s Dilemma game , 2011 .

[31]  J. Kosik,et al.  Quantum Parrondo's game with random strategies¶ , 2007, 0704.2937.

[32]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[33]  J. Sladkowski,et al.  Quantum Prisoner’s Dilemma game on hypergraph networks , 2013 .