Abstract
We know that k -Uniform Nash is W[2]-Complete when we consider imitation symmetric win-lose games (with k as the parameter) even when we have two players. However, this paper provides positive results regarding Nash equilibria. We show that consideration of sparse games or limitations of the support result in fixed-parameter algorithms with respect to one parameter only for the k -Uniform Nash problem. That is, we show that a sample uniform Nash equilibrium in r-sparse imitation symmetric win-lose games is not as hard because it can be found in FPT time (i.e polynomial in the size of the game, but maybe exponential in r). Moreover, we show that, although NP-Complete, the problem of Best Nash Equilibrium is also fix-parameter tractable.
Original language | English |
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Title of host publication | Combinatorial Algorithms |
Editors | Costas S. Iliopoulos, William F. Smyth |
Publisher | Springer Berlin |
Pages | 121-124 |
Number of pages | 4 |
ISBN (Electronic) | 978-3-642-19222-7 |
ISBN (Print) | 978-3-642-19221-0 |
DOIs | |
Publication status | Published - 2011 |
Externally published | Yes |
Event | International Workshop on Combinatorial Algorithms - London, United Kingdom Duration: 26 Jul 2010 → 28 Jul 2010 Conference number: 21st |
Publication series
Name | Lecture Notes in Computer Science |
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Publisher | Springer |
Volume | 6460 |
ISSN (Print) | 0302-9743 |
Conference
Conference | International Workshop on Combinatorial Algorithms |
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Abbreviated title | IWOCA 2010 |
Country/Territory | United Kingdom |
City | London |
Period | 26/07/10 → 28/07/10 |