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The Kolkata Paise Restaurant problem and resource utilization

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  • Chakrabarti, Anindya Sundar
  • Chakrabarti, Bikas K.
  • Chatterjee, Arnab
  • Mitra, Manipushpak

Abstract

We study the dynamics of the “Kolkata Paise Restaurant problem”. The problem is the following: In each period, N agents have to choose between N restaurants. Agents have a common ranking of the restaurants. Restaurants can only serve one customer. When more than one customer arrives at the same restaurant, one customer is chosen at random and is served; the others do not get the service. We first introduce the one-shot versions of the Kolkata Paise Restaurant problem which we call one-shot KPR games. We then study the dynamics of the Kolkata Paise Restaurant problem (which is a repeated game version of any given one shot KPR game) for large N. For statistical analysis, we explore the long time steady state behavior. In many such models with myopic agents we get under-utilization of resources, that is, we get a lower aggregate payoff compared to the social optimum. We study a number of myopic strategies, focusing on the average occupation fraction of restaurants.

Suggested Citation

  • Chakrabarti, Anindya Sundar & Chakrabarti, Bikas K. & Chatterjee, Arnab & Mitra, Manipushpak, 2009. "The Kolkata Paise Restaurant problem and resource utilization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(12), pages 2420-2426.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:12:p:2420-2426
    DOI: 10.1016/j.physa.2009.02.039
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    Cited by:

    1. Anindya S. Chakrabarti & Diptesh Ghosh, 2019. "Emergence of anti-coordination through reinforcement learning in generalized minority games," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(2), pages 225-245, June.
    2. Biswas, Soumyajyoti & Mandal, Amit Kr, 2021. "Parallel Minority Game and it’s application in movement optimization during an epidemic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    3. Priel, Avner & Tamir, Boaz, 2018. "Econophysics of a ranked demand and supply resource allocation problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 745-753.
    4. Chellig, Jordan & Durbac, Calina & Fountoulakis, Nikolaos, 2022. "Best response dynamics on random graphs," Games and Economic Behavior, Elsevier, vol. 131(C), pages 141-170.
    5. Vee-Liem Saw & Lock Yue Chew, 2020. "No-boarding buses: Synchronisation for efficiency," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-34, March.
    6. Karaenke, Paul & Bichler, Martin & Merting, Soeren & Minner, Stefan, 2020. "Non-monetary coordination mechanisms for time slot allocation in warehouse delivery," European Journal of Operational Research, Elsevier, vol. 286(3), pages 897-907.
    7. Ghosh, Diptesh & Chakrabarti, Anindya S., 2017. "Emergence of distributed coordination in the Kolkata Paise Restaurant problem with finite information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 16-24.
    8. Xu, C. & Gu, G.-Q. & Hui, P.M., 2024. "Impacts of an expert’s opinion on the collective performance of a competing population for limited resources," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    9. Zhong, Li-Xin & Xu, Wen-Juan & Ren, Fei & Shi, Yong-Dong, 2013. "Coupled effects of market impact and asymmetric sensitivity in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2139-2149.
    10. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: II. Agent-based models," Post-Print hal-00621059, HAL.
    11. Kiran Sharma & Anamika & Anindya S. Chakrabarti & Anirban Chakraborti & Sujoy Chakravarty, 2017. "The Saga of KPR: Theoretical and Experimental developments," Papers 1712.06358, arXiv.org.
    12. Chakrabarti, Anindya S. & Ghosh, Diptesh, 2016. "Improving Server Utilization in a Distributed Computing Set-up with Independent Clients," IIMA Working Papers WP2016-05-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    13. Kalliopi Kastampolidou & Christos Papalitsas & Theodore Andronikos, 2022. "The Distributed Kolkata Paise Restaurant Game," Games, MDPI, vol. 13(3), pages 1-21, April.
    14. Kalliopi Kastampolidou & Christos Papalitsas & Theodore Andronikos, 2021. "DKPRG or how to succeed in the Kolkata Paise Restaurant gamevia TSP," Papers 2101.07760, arXiv.org.
    15. Hardik Rajpal & Deepak Dhar, 2018. "Achieving Perfect Coordination amongst Agents in the Co-Action Minority Game," Games, MDPI, vol. 9(2), pages 1-13, May.

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