Dynamic Inventory Management with Mean-Field Competition

Ryan Donnelly; Sylvia Li

doi:10.1080/1350486X.2025.2488769

Dynamic Inventory Management with Mean-Field Competition

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Abstract

Agents attempt to maximize expected profits earned by selling multiple units of a perishable product where their revenue streams are affected by the prices they quote as well as the distribution of other prices quoted in the market by other agents. We propose a model which captures this competitive effect and directly analyse the model in the mean-field limit as the number of agents is very large. We classify mean-field Nash equilibrium in terms of the solution to a Hamilton-Jacobi-Bellman equation and a consistency condition and use this to motivate an iterative numerical algorithm. Convergence of this numerical algorithm yields the pricing strategy of a mean-field Nash equilibrium. Properties of the equilibrium pricing strategies and overall market dynamics are then investigated, in particular how they depend on the strength of the competitive interaction and the ability to oversell the product.

Original language	English
Pages (from-to)	279-311
Number of pages	33
Journal	Applied Mathematical Finance
Volume	31
Issue number	5
Early online date	7 May 2025
DOIs	https://doi.org/10.1080/1350486X.2025.2488769
Publication status	E-pub ahead of print - 7 May 2025

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Dynamic Inventory Management with Mean-Field Competition

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