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Receding Horizon Games for Modeling Competitive Supply Chains

Sophie Hall, Laura Guerrini, Florian Dörfler, Dominic Liao-McPherson

TL;DR

This paper introduces a receding horizon game (RHG) framework to model dynamic, competitive supply chains with multiple self-interested manufacturers. Each manufacturer solves a horizon-N generalized Nash equilibrium, and the open-loop equilibria are repeated over time with re-planning to form approximate closed-loop policies, enabling tractable analysis of complex dynamics, delays, and information asymmetry. Numerical studies show the approach can reproduce economically intuitive behaviors under demand spikes, supply shocks, and information asymmetry, including price signaling, reallocation of purchases, and advantages from forecast information. The RHG framework thus provides a practical, scalable method to study dynamic competition in supply chains and can inform policy design and regulation in real-world networks.

Abstract

The vast majority of products we use daily are supplied to us through complex global supply chains that transform raw materials into finished goods and distribute them to end consumers. This paper proposes a modeling methodology for dynamic competitive supply chains based on game theory and model predictive control. We model each manufacturer in the supply chain as a rational utility maximizing agent that selects their actions by finding an open-loop generalized Nash equilibrium of a multi-stage game. To react to competitors and the state of the market, every agent re-plans their actions in a receding horizon manner based on estimates of market and supplier parameters thereby creating an approximate closed-loop equilibrium policy. We demonstrate through numerical simulations that this modeling approach is computationally tractable and generates economically interpretable behaviors in a variety of settings such as demand spikes, supply shocks, and information asymmetry.

Receding Horizon Games for Modeling Competitive Supply Chains

TL;DR

This paper introduces a receding horizon game (RHG) framework to model dynamic, competitive supply chains with multiple self-interested manufacturers. Each manufacturer solves a horizon-N generalized Nash equilibrium, and the open-loop equilibria are repeated over time with re-planning to form approximate closed-loop policies, enabling tractable analysis of complex dynamics, delays, and information asymmetry. Numerical studies show the approach can reproduce economically intuitive behaviors under demand spikes, supply shocks, and information asymmetry, including price signaling, reallocation of purchases, and advantages from forecast information. The RHG framework thus provides a practical, scalable method to study dynamic competition in supply chains and can inform policy design and regulation in real-world networks.

Abstract

The vast majority of products we use daily are supplied to us through complex global supply chains that transform raw materials into finished goods and distribute them to end consumers. This paper proposes a modeling methodology for dynamic competitive supply chains based on game theory and model predictive control. We model each manufacturer in the supply chain as a rational utility maximizing agent that selects their actions by finding an open-loop generalized Nash equilibrium of a multi-stage game. To react to competitors and the state of the market, every agent re-plans their actions in a receding horizon manner based on estimates of market and supplier parameters thereby creating an approximate closed-loop equilibrium policy. We demonstrate through numerical simulations that this modeling approach is computationally tractable and generates economically interpretable behaviors in a variety of settings such as demand spikes, supply shocks, and information asymmetry.
Paper Structure (11 sections, 1 theorem, 23 equations, 8 figures, 1 table)

This paper contains 11 sections, 1 theorem, 23 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Setting
  3. Game-theoretic MPC-based modeling
  4. Numerical studies
  5. Demand spike
  6. Supply shock
  7. Information asymmetry: Demand forecast
  8. Information asymmetry: Market coupling
  9. Turnpike of the open-loop trajectories
  10. Conclusion
  11. Acknowledgements

Key Result

Lemma 1

Let $(\bar{u}, \bar{\lambda})$ satisfy eq:KKT and $\mathcal{A} = \{i~|~G_i \bar{u} = g_i(\bar{x})\}$ denote the active constraints at $\bar{u}$. Then if $y^T H y > 0$ for all $y \in \{u~|~ G_i u = 0,~i\in \mathcal{A}\}$ and rank $((G_i)_{i\in \mathcal{A}}) = \textrm{cardinality}(\mathcal{A})$, where

Figures (8)

  • Figure 1: A supply chain consisting of two upstream suppliers, three manufacturers, and a competitive downstream market.
  • Figure 2: A block diagram of the inventory dynamics of $M^1$, where $z$ denotes the forward shift operator.
  • Figure 3: A spike in base demand $w_t^v$ by a factor of two for manufacturers $M^1$ and $M^2$ for $t\in \mathbb{Z}_{[10,18]}$. The manufacturers have no preview of the demand spike.
  • Figure 4: A sudden drop of $70\%$ in the supply capacity $\bar{O}^1$ of supplier $S^1$ for $t\in \mathbb{Z}_{[10,18]}$.
  • Figure 5: Information asymmetry: Case (i) $M^1$ has perfect forecast of the demand spike and $M^2$ has no forecast; Case (ii) none of the manufacturers have forecast.
  • ...and 3 more figures

Theorems & Definitions (2)

  • Remark 1
  • Lemma 1