IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2506.17239.html
   My bibliography  Save this paper

Price equilibria with positive margins in loyal-strategic markets with discrete prices

Author

Listed:
  • Gurkirat Wadhwa
  • Akansh Verma
  • Veeraruna Kavitha
  • Priyank Sinha

Abstract

In competitive supply chains (SCs), pricing decisions are crucial, as they directly impact market share and profitability. Traditional SC models often assume continuous pricing for mathematical convenience, overlooking the practical reality of discrete price increments driven by currency constraints. Additionally, customer behavior, influenced by loyalty and strategic considerations, plays a significant role in purchasing decisions. To address these gaps, this study examines a SC model involving one supplier and two manufacturers, incorporating realistic factors such as customer demand segmentation and discrete price setting. Our analysis shows that the Nash equilibria (NE) among manufacturers are not unique, we then discuss the focal equilibrium. Our analysis also reveals that low denomination factors can lead to instability as the corresponding game does not have NE. Numerical simulations demonstrate that even small changes in price increments significantly affect the competitive dynamics and market share distribution.

Suggested Citation

  • Gurkirat Wadhwa & Akansh Verma & Veeraruna Kavitha & Priyank Sinha, 2025. "Price equilibria with positive margins in loyal-strategic markets with discrete prices," Papers 2506.17239, arXiv.org.
    • Handle: RePEc:arx:papers:2506.17239
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2506.17239
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-599, May.
    2. Changwen Li & Bin Cao & Yong-Wu Zhou & T. C. Edwin Cheng, 2023. "Pricing, coalition stability, and profit allocation in the pull assembly supply chains under competition," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(3), pages 977-1011, September.
    3. Marc Escrihuela-Villar & Jorge Guillén, 2025. "On Cournot and Bertrand competition in collusive mixed oligopolies," Journal of Economics, Springer, vol. 144(3), pages 231-246, April.
    Full references (including those not matched with items on IDEAS)

    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. Elliott, Robert & Sun, Puyang & Zhu, Tong, 2020. "Shell shocked: The impact of foreign entry on the gasoline retail market in China," Energy Economics, Elsevier, vol. 86(C).
    2. Allen, Beth & Thisse, Jacques-Francois, 1992. "Price Equilibria in Pure Strategies for Homogeneous Oligopoly," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 1(1), pages 63-81, Spring.
    3. Fullerton, Thomas M. & Jiménez, Alan A. & Walke, Adam G., 2015. "An econometric analysis of retail gasoline prices in a border metropolitan economy," The North American Journal of Economics and Finance, Elsevier, vol. 34(C), pages 450-461.
    4. Roy Chowdhury, Prabal, 2008. "Bertrand-Edgeworth equilibrium with a large number of firms," International Journal of Industrial Organization, Elsevier, vol. 26(3), pages 746-761, May.
    5. Wein, Thomas, 2021. "Why abandoning the paradise? Stations incentives to reduce gasoline prices at first," VfS Annual Conference 2021 (Virtual Conference): Climate Economics 242362, Verein für Socialpolitik / German Economic Association.
    6. Boone, J., 2004. "Balance of Power," Other publications TiSEM d3f8cd4b-eaf0-4c1c-aed4-5, Tilburg University, School of Economics and Management.
    7. Lau, Sau-Him Paul, 2001. "Aggregate Pattern of Time-dependent Adjustment Rules, II: Strategic Complementarity and Endogenous Nonsynchronization," Journal of Economic Theory, Elsevier, vol. 98(2), pages 199-231, June.
    8. Luís Cabral, 2018. "We’re Number 1: Price Wars for Market Share Leadership," Management Science, INFORMS, vol. 64(5), pages 2013-2030, May.
    9. Prabal Roy Chowdhury, 2004. "Bertrand-Edgeworth duopoly with linear costs: A tale of two paradoxes," Discussion Papers 04-13, Indian Statistical Institute, Delhi.
    10. Benjamin Atkinson, Andrew Eckert, and Douglas S. West, 2014. "Daily Price Cycles and Constant Margins: Recent Events in Canadian Gasoline Retailing," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3).
    11. Boone, Jan, 2004. "Balance of Power," CEPR Discussion Papers 4733, C.E.P.R. Discussion Papers.
    12. Perdiguero, Jordi & Jiménez, Juan Luis, 2021. "Price coordination in the Spanish oil market: The monday effect," Energy Policy, Elsevier, vol. 149(C).
    13. repec:cdl:agrebk:qt2g56n1jk is not listed on IDEAS
    14. Tiffany Ding & Dominique Perrault-Joncas & Orit Ronen & Michael I. Jordan & Dirk Bergemann & Dean Foster & Omer Gottesman, 2025. "Marketplace Operators Can Induce Competitive Pricing," Papers 2503.06582, arXiv.org, revised Oct 2025.
    15. Andreoli-Versbach, Patrick & Franck, Jens-Uwe, 2015. "Endogenous price commitment, sticky and leadership pricing: Evidence from the Italian petrol market," International Journal of Industrial Organization, Elsevier, vol. 40(C), pages 32-48.
    16. Do, Jihwan & Miklós-Thal, Jeanine, 2023. "Partial secrecy in vertical contracting," International Journal of Industrial Organization, Elsevier, vol. 90(C).
    17. David P.Byrne & Roger Ware, 2011. "Price Cycles and Price Leadership in Gasoline Markets: New Evidence from Canada," Department of Economics - Working Papers Series 1124, The University of Melbourne.
    18. Manuel Frondel & Colin Vance & Alex Kihm, 2016. "Time lags in the pass-through of crude oil prices: big data evidence from the German gasoline market," Applied Economics Letters, Taylor & Francis Journals, vol. 23(10), pages 713-717, July.
    19. Jayakumar Subramanian & Amit Sinha & Aditya Mahajan, 2023. "Robustness and Sample Complexity of Model-Based MARL for General-Sum Markov Games," Dynamic Games and Applications, Springer, vol. 13(1), pages 56-88, March.
    20. Shota Fujishima, 2015. "The emergence of cooperation through leadership," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 17-36, February.
    21. Øystein Foros & Mai Nguyen-Ones & Frode Steen, 2021. "The Effects of a Day off from Retail Price Competition: Evidence on Consumer Behavior and Firm Performance in Gasoline Retailing," International Journal of the Economics of Business, Taylor & Francis Journals, vol. 28(1), pages 49-87, January.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:2506.17239. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.