# Finding Optimal Strategies in a Multi-Period Multi-Leader-Follower Stackelberg Game Using an Evolutionary Algorithm

arXiv: https://arxiv.org/abs/1307.6246 · HTML: https://mlsanity.com/paper/1307.6246/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jul 2013.

## Built on by (most cited first, 4 of 4)

- [Oracles & Followers: Stackelberg Equilibria in Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2210.11942/) (2022)
- [The Data Minimization Principle in Machine Learning](https://mlsanity.com/paper/2405.19471/) (2024)
- [Bilevel Optimization for Neural Architecture Search](https://mlsanity.com/paper/2606.29582/) (2026)
- [A Linear Programming Enhanced Genetic Algorithm for Hyperparameter Tuning in Machine Learning](https://mlsanity.com/paper/2407.00613/) (2024)

## Abstract (arXiv)

Stackelberg games are a classic example of bilevel optimization problems, which are often encountered in game theory and economics. These are complex problems with a hierarchical structure, where one optimization task is nested within the other. Despite a number of studies on handling bilevel optimization problems, these problems still remain a challenging territory, and existing methodologies are able to handle only simple problems with few variables under assumptions of continuity and differentiability. In this paper, we consider a special case of a multi-period multi-leader-follower Stackelberg competition model with non-linear cost and demand functions and discrete production variables. The model has potential applications, for instance in aircraft manufacturing industry, which is an oligopoly where a few giant firms enjoy a tremendous commitment power over the other smaller players. We solve cases with different number of leaders and followers, and show how the entrance or exit of a player affects the profits of the other players. In the presence of various model complexities, we use a computationally intensive nested evolutionary strategy to find an optimal solution for the model. The strategy is evaluated on a test-suite of bilevel problems, and it has been shown that the method is successful in handling difficult bilevel problems.