When Nash Meets Stackelberg

• 成果类型: Article
• 署名作者: Carvalho, Margarida; Dragotto, Gabriele; Feijoo, Felipe; Lodi, Andrea; Sankaranarayanan, Sriram
• 署名单位: Universite de Montreal; Universite de Montreal; Princeton University; Technion Israel Institute of Technology; Indian Institute of Management (IIM System); Indian Institute of Management Ahmedabad
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2022.03418
• 发表日期: 2024
• 页码: 7308-7324
• 关键词: Algorithmic game theory; integer programming; bilevel optimization; Stackelberg game

摘要

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 sigma p2-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.