# When Nash Meets Stackelberg

arXiv: https://arxiv.org/abs/1910.06452 · HTML: https://mlsanity.com/paper/1910.06452/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2019.

## Built on by (most cited first, 2 of 2)

- [Machine Learning-Augmented Optimization of Large Bilevel and Two-stage Stochastic Programs: Application to Cycling Network Design](https://mlsanity.com/paper/2209.09404/) (2022)
- [Who Plays First? Optimizing the Order of Play in Stackelberg Games with Many Robots](https://mlsanity.com/paper/2402.09246/) (2024)

## Abstract (arXiv)

This article introduces a class of Nash games among Stackelberg players (NASPs), namely, a class of simultaneous non-cooperative games where the players solve sequential Stackelberg games. Specifically, each player solves a Stackelberg game where a leader optimizes a (parametrized) linear objective function subject to linear constraints while its followers solve convex quadratic problems subject to the standard optimistic assumption. Although we prove that deciding if a NASP instance admits a Nash equilibrium is generally a Sigma2p-hard decision problem, we devise two exact and computationally-efficient algorithms to compute and select Nash equilibria or certify that no equilibrium exists. We apply NASPs to model the hierarchical interactions of international energy markets where climate-change aware regulators oversee the operations of profit-driven energy producers. By combining real-world data with our models, we find that Nash equilibria provide informative, and often counterintuitive, managerial insights for market regulators.