Inventory competition in a multi channel distribution system: The Nash and Stackelberg game

TL;DR

This paper analyzes inventory management strategies in a multi-channel distribution system with one manufacturer and multiple retailers, establishing conditions for unique Nash and Stackelberg equilibria and comparing outcomes.

Contribution

It proves the existence and uniqueness conditions for Nash and Stackelberg equilibria in a stochastic demand setting with multiple retailers.

Findings

Manufacturer carries more inventory when prices equal production costs.

Unique equilibrium conditions are derived for both Nash and Stackelberg games.

Comparison shows different inventory levels under various game structures.

Abstract

This paper investigates inventory management in a multi channel distribution system consisting of one manufacturer and an arbitrary number of retailers that face stochastic demand. Existence of the pure Nash equilibrium is proved and parameter restriction which implies uniqueness of it is derived. Also the Stackelberg game where the manufacturer plays a roll as a leader is discussed. Under specified parameter restrictions which guarantee profitability, sufficient condition for uniqueness of Stackelberg equilibrium is obtained. In addition comparison with simultaneous move game is made. The result shows that when whole prices are equal to production cost, manufacturer carries more inventory than simultaneous move game. Keywords: Inventory management, Substitution, Nash equilibrium, Stackelberg equilibrium.