Paper: arXiv 2506.17239

Authors: 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.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a sophisticated theoretical framework combining a three-level game with mean-field game theory and discrete Bertrand competition to analyze supply chain pricing. However, it relies almost entirely on analytical derivations and basic numerical simulations without empirical data validation or market backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Analyze competitive SC dynamics with discrete pricing & loyal-strategic customers] --> B[Inputs: 1 Supplier, 2 Manufacturers, Customer Segmentation, Currency Constraints]
    B --> C[Methodology: Game Theoretic SC Model with Discrete Price Increments]
    C --> D[Computational Process: Derive Nash Equilibria & Simulate Price Increment Changes]
    D --> E[Outcome 1: Multiple NE Exist; Focal Equilibrium Identified]
    D --> F[Outcome 2: Low Denomination Factors Cause Instability / No NE]
    D --> G[Outcome 3: Small Increment Changes Significantly Alter Market Share & Dynamics]

Cited References (23)

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and 15 more
  1. Coalition Formation for Horizontal Supply Chain Collaboration: A Multiobjective Approach (2022)
  2. The potential of cooperative game theory for supply chain management (2005)
  3. Pricing, coalition stability, and profit allocation in the pull assembly supply chains under competition (2023)
  4. Coalition stability in assembly models (2009)
  5. Competition and cooperation in decentralized push and pull assembly systems (2008)
  6. Supply chain coordination with contracts (2003)
  7. Information sharing and supply chain coordination (2003)
  8. Supply chain coordination with demand disruptions (2004)
  9. Cooperative games with coalition structures (1974)
  10. A review on supply chain coordination: coordination mechanisms, managing uncertainty and research directions (2011)
  11. Stable farsighted coalitions in competitive markets (2007)
  12. Game theory in supply chain analysis (2006)
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  14. A general framework for the study of decentralized distribution systems (2001)
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0 of 23 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.