How Well Do People Play a Quantum Prisoner’s Dilemma?

Game theory suggests quantum information processing technologies could provide useful new economic mechanisms. For example, using shared entangled quantum states can alter incentives so as to reduce the free-rider problem inherent in economic contexts such as public goods provisioning. However, game theory assumes players understand fully the consequences of manipulating quantum states and are rational. Its predictions do not always describe human behavior accurately. To evaluate the potential practicality of quantum economic mechanisms, we experimentally tested how people play the quantum version of the prisoner’s dilemma game in a laboratory setting using a simulated version of the underlying quantum physics. Even without formal training in quantum mechanics, people nearly achieve the payoffs theory predicts, but do not use mixed-strategy Nash equilibria predicted by game theory. Moreover, this correspondence with game theory for the quantum game is closer than that of the classical game.

[1]  Colin Camerer Individual Decision Making , 2020, The Handbook of Experimental Economics.

[2]  Robert Axelrod,et al.  The Evolution of Strategies in the Iterated Prisoner's Dilemma , 2001 .

[3]  G. Hardin,et al.  The Tragedy of the Commons , 1968, Green Planet Blues.

[4]  Li Zhang,et al.  REDUCED ENTANGLEMENT FOR QUANTUM GAMES , 2003 .

[5]  Colin Camerer,et al.  A Cognitive Hierarchy Model of Games , 2004 .

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

[7]  Tad Hogg,et al.  A Quantum Treatment of Public Goods Economics , 2002, Quantum Inf. Process..

[8]  H. Rosenthal,et al.  Digitized by the Internet Archive in 2011 With^ Funding from Testing Game-theoretic Models of Free Riding: New Evidence on Probability Bias and Learning , 2022 .

[9]  Jiangfeng Du,et al.  Experimental realization of quantum games on a quantum computer. , 2001, Physical Review Letters.

[10]  Jens Eisert,et al.  Quantum games , 2020, Understanding Game Theory.

[11]  Hui Li,et al.  Entanglement enhanced multiplayer quantum games , 2002 .

[12]  R. Thaler The Ultimatum Game , 1988 .

[13]  Barton L. Lipman,et al.  Provision of Public Goods: Fully Implementing the Core through Private Contributions , 1989 .

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

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

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

[17]  B. Huberman,et al.  THE DYNAMICS OF SOCIAL DILEMMAS , 1994 .

[18]  A. Hibbs QED: The Strange Theory of Light and Matter , 1986 .

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

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

[21]  J. Kagel,et al.  Handbook of Experimental Economics , 1997 .

[22]  J. Ledyard Public Goods: A Survey of Experimental Research , 1994 .

[23]  David A. Meyer,et al.  Quantum Communication in Games , 2004 .

[24]  T. Groves,et al.  Optimal Allocation of Public Goods: A Solution to the 'Free Rider Problem' , 1977 .

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

[26]  S. T. Buckland,et al.  Computer-Intensive Methods for Testing Hypotheses. , 1990 .