When Nash Meets Stackelberg

Margarida Carvalho (), Gabriele Dragotto (), Felipe Feijoo (), Andrea Lodi () and Sriram Sankaranarayanan ()
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Margarida Carvalho: CIRRELT and Département d’Informatique et de Recherche Opérationnelle, Université de Montréal, Montréal, Quebec H3T 1J4, Canada
Gabriele Dragotto: Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544
Felipe Feijoo: School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2340025, Chile
Andrea Lodi: Jacobs Technion-Cornell Institute, Cornell Tech and Technion – IIT, New York City, New York 10044
Sriram Sankaranarayanan: Operations and Decision Sciences, Indian Institute of Management, Ahmedabad 380015, Gujarat, India

Management Science, 2024, vol. 70, issue 10, 7308-7324

Abstract: This article introduces a class of Nash games among Stackelberg players (NASPs), namely, a class of simultaneous noncooperative 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, whereas 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 Σ 2 p -hard decision problem, we devise two exact and computationally efficient algorithms to compute and select Nash equilibria or certify that no equilibrium exists. We use 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.

Keywords: algorithmic game theory; integer programming; bilevel optimization; Stackelberg game (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:70:y:2024:i:10:p:7308-7324

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