Dynamic Inventory Management with Mean-Field Competition

34 Pages Posted: 9 Nov 2022

See all articles by Ryan Francis Donnelly

Ryan Francis Donnelly

King's College London

Zi Li

King’s College London

Date Written: October 31, 2022

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 analyze 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 to compute 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.

Keywords: mean-field game, dynamic pricing, optimal control

JEL Classification: C61, C73, G11

Suggested Citation

Donnelly, Ryan Francis and Li, Zi, Dynamic Inventory Management with Mean-Field Competition (October 31, 2022). Available at SSRN: https://ssrn.com/abstract=4262719 or http://dx.doi.org/10.2139/ssrn.4262719

Ryan Francis Donnelly (Contact Author)

King's College London ( email )

Strand
London, England WC2R 2LS
United Kingdom

Zi Li

King’s College London ( email )

Strand
London, England WC2R 2LS
United Kingdom

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