Quantum Nash equilibrium in the thermodynamic limit

  • Shubhayan Sarkar
  • Colin BenjaminEmail author


The quantum Nash equilibrium in the thermodynamic limit is studied for games like quantum Prisoner’s dilemma and quantum game of Chicken. A phase transition is seen in both games as function of the entanglement in the game. We observe that for maximal entanglement irrespective of the classical payoffs, majority of players choose quantum strategy over defect in the thermodynamic limit.


Quantum games Hawk–Dove game Nash equilibrium 



This work was supported by the Grant “Non-local correlations in nanoscale systems: Role of decoherence, interactions, disorder and pairing symmetry” from SCIENCE & ENGINEERING RESEARCH BOARD, New Delhi, Government of India, Grant No. EMR/20l5/001836, Principal Investigator: Dr. Colin Benjamin, National Institute of Science Education and Research, Bhubaneswar, India. CB thanks Condensed matter and Statistical Physics section of the Abdus Salam ICTP, Trieste, Italy, for funding a research visit during which a part of this work was completed.

Author Contributions

CB conceived the proposal, SS did the calculations on the advice of CB. CB and SS analyzed the results and wrote the paper. Both authors reviewed the manuscript.

Compliance with ethical standards

Conflict of interest

The authors have no potential financial or non-financial conflicts of interest.

Data availability statement

All data generated or analyzed during this study are included in this manuscript.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Physical SciencesNational Institute of Science Education and Research, HBNIJatniIndia

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