IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v193y2017icp726-736.html
   My bibliography  Save this article

On the uniqueness and stability of equilibrium in quality-speed competition with boundedly-rational customers: The case with general reward function and multiple servers

Author

Listed:
  • Li, Xin
  • Li, Qingying
  • Guo, Pengfei
  • Lian, Zhaotong

Abstract

In this paper, we extend the service-speed competition game with boundedly rational customers considered in Li et al. (2016) to the case with general reward function and multiple servers. The N servers make strategic decisions on their service rates sequentially and repeatedly. Since the competing servers' payoff functions can only be expressed by an implicit-function set, we propose a matrix method to derive the uniqueness of the equilibrium service rates, and we establish the stability of the equilibrium through a tatônnement scheme. By conducting a sensitivity analysis regarding the number of competing servers and the demand density, we find that the server competition benefits the customers by improving their utilities as well as getting more customers to be served. Furthermore, for a fixed demand density, the equilibrium service rate increases in the market size and converges to a certain level when the market size is large enough.

Suggested Citation

  • Li, Xin & Li, Qingying & Guo, Pengfei & Lian, Zhaotong, 2017. "On the uniqueness and stability of equilibrium in quality-speed competition with boundedly-rational customers: The case with general reward function and multiple servers," International Journal of Production Economics, Elsevier, vol. 193(C), pages 726-736.
    • Handle: RePEc:eee:proeco:v:193:y:2017:i:c:p:726-736
    DOI: 10.1016/j.ijpe.2017.08.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925527317302797
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ijpe.2017.08.026?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ginsburgh, Victor & Waelbroeck, Jean, 1979. "A Note on the Simultaneous Stability of Tatonnement Processes for Computing Equilibria," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(2), pages 367-380, June.
    2. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    3. Song, Yanan & Zhao, Xiaobo, 2016. "Strategic customer behavior facing possible stockout: An experimental study," International Journal of Production Economics, Elsevier, vol. 180(C), pages 57-67.
    4. Tingliang Huang & Gad Allon & Achal Bassamboo, 2013. "Bounded Rationality in Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 263-279, May.
    5. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
    6. Xin Li & Pengfei Guo & Zhaotong Lian, 2016. "Quality-Speed Competition in Customer-Intensive Services with Boundedly Rational Customers," Production and Operations Management, Production and Operations Management Society, vol. 25(11), pages 1885-1901, November.
    7. Ehud Kalai & Morton I. Kamien & Michael Rubinovitch, 1992. "Optimal Service Speeds in a Competitive Environment," Management Science, INFORMS, vol. 38(8), pages 1154-1163, August.
    8. Nagurney, Anna & Li, Dong & Nagurney, Ladimer S., 2014. "Spatial price equilibrium with information asymmetry in quality and minimum quality standards," International Journal of Production Economics, Elsevier, vol. 158(C), pages 300-313.
    9. Tingliang Huang & Ying-Ju Chen, 2015. "Service Systems with Experience-Based Anecdotal Reasoning Customers," Production and Operations Management, Production and Operations Management Society, vol. 24(5), pages 778-790, May.
    10. Hefti, Andreas, 2016. "On the relationship between uniqueness and stability in sum-aggregative, symmetric and general differentiable games," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 83-96.
    11. Tingliang Huang & Qian Liu, 2015. "Strategic Capacity Management When Customers Have Boundedly Rational Expectations," Production and Operations Management, Production and Operations Management Society, vol. 24(12), pages 1852-1869, December.
    12. Krishnan S. Anand & M. Faz{i}l Paç & Senthil Veeraraghavan, 2011. "Quality-Speed Conundrum: Trade-offs in Customer-Intensive Services," Management Science, INFORMS, vol. 57(1), pages 40-56, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Canbolat, Pelin G., 2020. "Bounded rationality in clearing service systems," European Journal of Operational Research, Elsevier, vol. 282(2), pages 614-626.
    2. Bin Shen & Yanhui Deng & Xin Wang & Qingying Li, 2020. "Overstated product sustainability: real cases and a game-theoretical analysis," Annals of Operations Research, Springer, vol. 291(1), pages 779-797, August.
    3. Niu, Baozhuang & Xu, Haotao & Chen, Lei, 2022. "Creating all-win by blockchain in a remanufacturing supply chain with consumer risk-aversion and quality untrust," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 163(C).
    4. Jinting Wang & Ke Sun, 2022. "Optimal pricing and capacity sizing for online service systems with free trials," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(1), pages 57-86, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xin Li & Pengfei Guo & Zhaotong Lian, 2017. "Price and capacity decisions of service systems with boundedly rational customers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(6), pages 437-452, September.
    2. Jordan Tong & Daniel Feiler, 2017. "A Behavioral Model of Forecasting: Naive Statistics on Mental Samples," Management Science, INFORMS, vol. 63(11), pages 3609-3627, November.
    3. Tingliang Huang & Zhe Yin & Ying-Ju Chen, 2017. "Managing Posterior Price Matching: The Role of Customer Boundedly Rational Expectations," Manufacturing & Service Operations Management, INFORMS, vol. 19(3), pages 385-402, July.
    4. Qiao‐Chu He & Ying‐Ju Chen & Rhonda Righter, 2020. "Learning with Projection Effects in Service Operations Systems," Production and Operations Management, Production and Operations Management Society, vol. 29(1), pages 90-100, January.
    5. Jinting Wang & Ke Sun, 2022. "Optimal pricing and capacity sizing for online service systems with free trials," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(1), pages 57-86, March.
    6. Canbolat, Pelin G., 2020. "Bounded rationality in clearing service systems," European Journal of Operational Research, Elsevier, vol. 282(2), pages 614-626.
    7. Dongyuan Zhan & Amy R. Ward, 2019. "Staffing, Routing, and Payment to Trade off Speed and Quality in Large Service Systems," Operations Research, INFORMS, vol. 67(6), pages 1738-1751, November.
    8. Mirko Kremer & Laurens Debo, 2016. "Inferring Quality from Wait Time," Management Science, INFORMS, vol. 62(10), pages 3023-3038, October.
    9. Jalili Marand, Ata & Tang, Ou & Li, Hongyan, 2019. "Quandary of service logistics: Fast or reliable?," European Journal of Operational Research, Elsevier, vol. 275(3), pages 983-996.
    10. Caner Canyakmaz & Tamer Boyaci, 2018. "Queueing systems with rationally inattentive customers," ESMT Research Working Papers ESMT-18-04_R1, ESMT European School of Management and Technology, revised 01 Oct 2020.
    11. Suresh P. Sethi & Sushil Gupta & Vipin K. Agrawal & Vijay K. Agrawal, 2022. "Nobel laureates’ contributions to and impacts on operations management," Production and Operations Management, Production and Operations Management Society, vol. 31(12), pages 4283-4303, December.
    12. Sezer Ülkü & Chris Hydock & Shiliang Cui, 2020. "Making the Wait Worthwhile: Experiments on the Effect of Queueing on Consumption," Management Science, INFORMS, vol. 66(3), pages 1149-1171, March.
    13. Gregory DeCroix & Xiaoyang Long & Jordan Tong, 2021. "How Service Quality Variability Hurts Revenue When Customers Learn: Implications for Dynamic Personalized Pricing," Operations Research, INFORMS, vol. 69(3), pages 683-708, May.
    14. Barthel, Anne-Christine & Hoffmann, Eric, 2023. "On the existence of stable equilibria in monotone games," Journal of Mathematical Economics, Elsevier, vol. 105(C).
    15. Laurens Debo & Senthil Veeraraghavan, 2014. "Equilibrium in Queues Under Unknown Service Times and Service Value," Operations Research, INFORMS, vol. 62(1), pages 38-57, February.
    16. Ming Hu & Yang Li & Jianfu Wang, 2018. "Efficient Ignorance: Information Heterogeneity in a Queue," Management Science, INFORMS, vol. 64(6), pages 2650-2671, June.
    17. Sun, Mingyao & Chai, Qiangfei & Ng, Chi To, 2023. "Managing the quality-speed tradeoff in blockchain-supported healthcare diagnostic services," Omega, Elsevier, vol. 120(C).
    18. Caner Canyakmaz & Tamer Boyaci, 2018. "Opaque queues: Service systems with rationally inattentive customers," ESMT Research Working Papers ESMT-18-04, ESMT European School of Management and Technology.
    19. Han Zhu & Yimin Yu & Saibal Ray, 2021. "Quality Disclosure Strategy under Customer Learning Opportunities," Production and Operations Management, Production and Operations Management Society, vol. 30(4), pages 1136-1153, April.
    20. Shiliang Cui & Senthil Veeraraghavan, 2016. "Blind Queues: The Impact of Consumer Beliefs on Revenues and Congestion," Management Science, INFORMS, vol. 62(12), pages 3656-3672, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:proeco:v:193:y:2017:i:c:p:726-736. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ijpe .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.