Online Learning in Supply-Chain Games

TL;DR

This paper investigates how a supplier and retailer can learn optimal strategies over time in a supply chain game with incomplete information, demonstrating convergence to equilibrium and providing regret bounds.

Contribution

It introduces a framework for online learning in supply-chain games, proving convergence to equilibrium under partial information and deriving finite-time regret bounds.

Findings

Convergence of strategies to the Stackelberg equilibrium with partial knowledge.

Finite-time bounds on supplier's regret and asymptotic bounds on retailer's regret.

Optimal regret bounds in the case of non-strategic supplier with adversarial costs and demand.

Abstract

We study a repeated game between a supplier and a retailer who want to maximize their respective profits without full knowledge of the problem parameters. After characterizing the uniqueness of the Stackelberg equilibrium of the stage game with complete information, we show that even with partial knowledge of the joint distribution of demand and production costs, natural learning dynamics guarantee convergence of the joint strategy profile of supplier and retailer to the Stackelberg equilibrium of the stage game. We also prove finite-time bounds on the supplier's regret and asymptotic bounds on the retailer's regret, where the specific rates depend on the type of knowledge preliminarily available to the players. In the special case when the supplier is not strategic (vertical integration), we prove optimal finite-time regret bounds on the retailer's regret (or, equivalently, the social welfare) when costs and demand are adversarially generated and the demand is censored.