Skip to main content

An Introduction to Multi-player, Multi-choice Quantum Games: Quantum Minority Games & Kolkata Restaurant Problems

  • Chapter
Econophysics of Systemic Risk and Network Dynamics

Part of the book series: New Economic Windows ((NEW))

Abstract

We give a self contained introduction to a few quantum game protocols, starting with the quantum version of the two-player two-choice game of Prisoners dilemma, followed by an n-player generalization trough the quantum minority games, and finishing with a contribution towards an n-player m-choice generalization with a quantum version of a three-player Kolkata restaurant problem. We have omitted some technical details accompanying these protocols, and instead laid the focus on presenting some general aspects of the field as a whole. This review contains an introduction to the formalism of quantum information theory, as well as to important game theoretical concepts, and is aimed to work as a review suiting economists and game theorists with limited knowledge of quantum physics as well as to physicists with limited knowledge of game theory.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Nielsen M, Chuang I (2000) Quantum computation and quantum information. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  2. Hargreaves Heap S, Varoufakis Y (2004) Game theory – a critical introduction. Routledge, London

    Google Scholar 

  3. Fudenberg D, Tirole J (1991) Game theory. MIT Press, Cambridge

    Google Scholar 

  4. Osbourne MJ, Rubinstein A (1994) A course in game theory. MIT Press, Cambridge

    Google Scholar 

  5. Flitney AP (2008) Review of quantum games. In: Haugen IN, Nilsen AS (eds) Game theory: strategies, equilibria, and theorems, p 140

    Google Scholar 

  6. Piotrowski EW, Sladkowski J (2003) An invitation to quantum game theory. Int J Theor Phys 42:1089

    Article  MathSciNet  MATH  Google Scholar 

  7. Khan FS, Phoenix SJD (2011) Nash equilibrium in quantum superpositions. In: Proceedings of SPIE, vol 8057 80570K-1

    Google Scholar 

  8. Landsburg SE (2011) Quantum game theory. Wiley encyclopedia of operations research and management science

    Google Scholar 

  9. Bleiler SA (2008) A formalism for quantum games and an application. Preprint http://arxiv.org/abs/0808.1389

  10. Marinatto L, Weber T (2000) A quantum approach to static games of complete information. Phys Lett A 272:291–303

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Meyer D (1999) Quantum strategies. Phys Rev Lett 82:1052–1055

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Eisert J, Wilkens M, Lewenstein M (1999) Quantum games and quantum strategies. Phys Rev Lett 83:3077–3080

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Benjamin S, Hayden P (2001) Multiplayer quantum games. Phys Rev A 64:030301

    Article  ADS  Google Scholar 

  14. Chen Q, Wang Y (2004) N-player quantum minority game. Phys Lett A 327(98):102

    ADS  Google Scholar 

  15. Flitney A, Hollenberg LCL (2007) Multiplayer quantum minority game with decoherence. Quantum Inf Comput 7:111–126

    MathSciNet  MATH  Google Scholar 

  16. Flitney A, Greentree A (2007) Coalitions in the quantum minority game: classical cheats and quantum bullies. Phys Lett A 362:132137

    Article  Google Scholar 

  17. Schmid C, Flitney AP, Wieczorek W, Kiesel N, Weinfurter H, Hollenberg LCL (2010) Experimental implementation of a four-player quantum game. New J Phys 12:063031

    Article  Google Scholar 

  18. Sharif P, Heydari H (2011) Quantum solution to a three player Kolkata restaurant problem using entangled qutrits. Preprint http://arxiv.org/abs/1111.1962

  19. Benjamin S, Hayden P (2001) Comment on quantum games and quantum strategies. Preprint http://arxiv.org/abs/quant-ph/0003036

  20. Chakrabarti BK (2007) Kolkata restaurant problem as a generalised El Farol Bar problem. In: Chatterjee A, Chakrabarti BK (eds) Econophysics of markets & business networks. New economic windows series. Springer, Milan, pp 239–246

    Chapter  Google Scholar 

  21. Chakrabarti AS, Chakrabarti BK, Chatterjee A, Mitra M (2009) The Kolkata paise restaurant problem and resource utilization. Physica A 388:2420–2426

    Article  ADS  Google Scholar 

  22. Ghosh A, Chakrabarti AS, Chakrabarti BK (2010) Kolkata paise restaurant problem in some uniform learning strategy limits. In: Basu B, Chakrabarti BK, Chakravarty SR, Gangopadhyay K (eds) Econophysics & economics of games, social choices & quantitative techniques, New economic windows. Springer, Milan, pp 3–9

    Chapter  Google Scholar 

  23. Ghosh A, Chatterjee A, Mitra M, Chakrabarti BK (2010) New J Phys 12:075033

    Article  Google Scholar 

  24. Arthur WB (1994) Inductive reasoning and bounded rationality: El Farol problem. Am Econ Assoc Papers & Proc 84:406

    Google Scholar 

  25. Mathur M, Sen D (2001) Coherent states for SU(3). J Math Phys 42:4181–4196

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Acknowledgements

The work was supported by the Swedish Research Council (VR).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Puya Sharif .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Italia

About this chapter

Cite this chapter

Sharif, P., Heydari, H. (2013). An Introduction to Multi-player, Multi-choice Quantum Games: Quantum Minority Games & Kolkata Restaurant Problems. In: Abergel, F., Chakrabarti, B., Chakraborti, A., Ghosh, A. (eds) Econophysics of Systemic Risk and Network Dynamics. New Economic Windows. Springer, Milano. https://doi.org/10.1007/978-88-470-2553-0_14

Download citation

Publish with us

Policies and ethics