# Online Learning in Supply-Chain Games

arXiv: https://arxiv.org/abs/2207.04054 · HTML: https://mlsanity.com/paper/2207.04054/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 32 references that are in the map.
- First posted on arXiv 8 Jul 2022.

## Builds on (most cited first, 6 of 6)

- [Nonstochastic Multi-Armed Bandits with Graph-Structured Feedback](https://mlsanity.com/paper/1409.8428/) (2014)
- [Strategizing against No-regret Learners](https://mlsanity.com/paper/1909.13861/) (2019)
- [Sample-Efficient Learning of Stackelberg Equilibria in General-Sum Games](https://mlsanity.com/paper/2102.11494/) (2021)
- [Strategizing against Learners in Bayesian Games](https://mlsanity.com/paper/2205.08562/) (2022)
- [Learning to Play Sequential Games versus Unknown Opponents](https://mlsanity.com/paper/2007.05271/) (2020)
- [Regret analysis of the Piyavskii-Shubert algorithm for global Lipschitz optimization](https://mlsanity.com/paper/2002.02390/) (2020)

## Abstract (arXiv)

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.