A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis
We provide a unified variational inequality framework for the study of fundamental properties of the Nash equilibrium in network games. We identify several conditions on the underlying network (in terms of spectral norm, infinity norm and minimum eigenvalue of its adjacency matrix) that guarantee ex...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Elsevier BV
2019
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| Online Access: | https://hdl.handle.net/1721.1/121465 |
| _version_ | 1811081575777959936 |
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| author | Parise, Francesca Ozdagalar, Asuman E. |
| author2 | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems |
| author_facet | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Parise, Francesca Ozdagalar, Asuman E. |
| author_sort | Parise, Francesca |
| collection | MIT |
| description | We provide a unified variational inequality framework for the study of fundamental properties of the Nash equilibrium in network games. We identify several conditions on the underlying network (in terms of spectral norm, infinity norm and minimum eigenvalue of its adjacency matrix) that guarantee existence, uniqueness, convergence and continuity of equilibrium in general network games with multidimensional and possibly constrained strategy sets. We delineate the relations between these conditions and characterize classes of networks that satisfy each of these conditions. Keywords: network games, variational inequalities, strong monotonicity, uniform P-function, Nash
equilibrium, existence and uniqueness, best response dynamics, sensitivity analysis |
| first_indexed | 2024-09-23T11:48:52Z |
| format | Article |
| id | mit-1721.1/121465 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:48:52Z |
| publishDate | 2019 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1214652022-09-27T22:05:17Z A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis Parise, Francesca Ozdagalar, Asuman E. Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science We provide a unified variational inequality framework for the study of fundamental properties of the Nash equilibrium in network games. We identify several conditions on the underlying network (in terms of spectral norm, infinity norm and minimum eigenvalue of its adjacency matrix) that guarantee existence, uniqueness, convergence and continuity of equilibrium in general network games with multidimensional and possibly constrained strategy sets. We delineate the relations between these conditions and characterize classes of networks that satisfy each of these conditions. Keywords: network games, variational inequalities, strong monotonicity, uniform P-function, Nash equilibrium, existence and uniqueness, best response dynamics, sensitivity analysis Swiss National Science Foundation (P2EZP2 168812) Swiss National Science Foundation (P300P2 177805) United States. Army Research Office. Multidisciplinary University Research Initiative (W911NF-12-1-0509) 2019-07-01T18:15:12Z 2019-07-01T18:15:12Z 2019-03 2019-06-28T16:52:18Z Article http://purl.org/eprint/type/JournalArticle 0899-8256 https://hdl.handle.net/1721.1/121465 Parise, Francesca, and Asuman Ozdaglar. “A Variational Inequality Framework for Network Games: Existence, Uniqueness, Convergence and Sensitivity Analysis.” Games and Economic Behavior 114 (March 2019): 47–82. en 10.1016/j.geb.2018.11.012 Games and Economic Behavior Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV arXiv |
| spellingShingle | Parise, Francesca Ozdagalar, Asuman E. A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis |
| title | A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis |
| title_full | A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis |
| title_fullStr | A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis |
| title_full_unstemmed | A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis |
| title_short | A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis |
| title_sort | variational inequality framework for network games existence uniqueness convergence and sensitivity analysis |
| url | https://hdl.handle.net/1721.1/121465 |
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