Abstract
We develop a quasi-polynomial time Las Vegas algorithm for approximating Nash equilibria in polymatrix games over trees, under a mild renormalizing assumption. Our result, in particular, leads to an expected polynomial-time algorithm for computing approximate Nash equilibria of tree polymatrix games in which the number of actions per player is a fixed constant. Further, for trees with constant degree, the running time of the algorithm matches the best known upper bound for approximating Nash equilibria in bimatrix games (Lipton, Markakis, and Mehta 2003). Notably, this work closely complements the hardness result of Rubinstein (2015), which establishes the inapproximability of Nash equilibria in polymatrix games over constant-degree bipartite graphs with two actions per player.
Original language | English |
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Title of host publication | Algorithmic Game Theory - 8th International Symposium, SAGT 2015 |
Editors | Martin Hoefer, Martin Hoefer |
Publisher | Springer Verlag |
Pages | 285-296 |
Number of pages | 12 |
ISBN (Print) | 9783662484326 |
DOIs | |
State | Published - 2015 |
Externally published | Yes |
Event | 8th International Symposium on Algorithmic Game Theory, SAGT 2015 - Saarbrucken, Germany Duration: 28 Sep 2015 → 30 Sep 2015 |
Publication series
Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9347 |
ISSN (Print) | 0302-9743 |
ISSN (Electronic) | 1611-3349 |
Conference
Conference | 8th International Symposium on Algorithmic Game Theory, SAGT 2015 |
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Country/Territory | Germany |
City | Saarbrucken |
Period | 28/09/15 → 30/09/15 |
Bibliographical note
Publisher Copyright:© Springer International Publishing Switzerland 2015.