When Nash Meets Stackelberg
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2019
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| Acceso en línea: | |
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| _version_ | 1866913715560906752 |
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| author | Carvalho, Margarida Dragotto, Gabriele Feijoo, Felipe Lodi, Andrea Sankaranarayanan, Sriram |
| author_facet | Carvalho, Margarida Dragotto, Gabriele Feijoo, Felipe Lodi, Andrea Sankaranarayanan, Sriram |
| contents | 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 $Σ^2_p$-hard decision problem, we devise two exact and computationally-efficient algorithms to compute and select Nash equilibria or certify that no equilibrium exists. We 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_06452 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | When Nash Meets Stackelberg Carvalho, Margarida Dragotto, Gabriele Feijoo, Felipe Lodi, Andrea Sankaranarayanan, Sriram Computer Science and Game Theory Optimization and Control 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 $Σ^2_p$-hard decision problem, we devise two exact and computationally-efficient algorithms to compute and select Nash equilibria or certify that no equilibrium exists. We 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. |
| title | When Nash Meets Stackelberg |
| topic | Computer Science and Game Theory Optimization and Control |
| url | https://arxiv.org/abs/1910.06452 |