Approximate Nash Equilibria under Stability Conditions

Finding approximate Nash equilibria in n × n bimatrix games is currently one of the main open problems in algorithmic game theory. Motivated in part by the lack of progress on worst case instances, Awasthi et. al [2] proposed the question of finding approximate Nash equilibria in games that satisfy a natural stability to approximation condition. In this paper, we substantially generalize their results, provide the first lower bounds known for such games, and develop connections to other interesting notions of stability. Our first main contribution is to show that the main upper bound of Awasthi et. al [2] applies to a substantially more general stability condition. In particular, rather than assuming that there exists a fixed Nash equilibrium (p∗ , q∗ ) such that all ǫ-approximate equilibria are contained in a ball of radius ∆ around (p∗ , q∗ ) (as in the Awasthi et. al [2] work), we require only that for any ǫ-approximateequilibrium (p, q) there exists a Nash equilib...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Maria-Florina Balcan, Mark Braverman
• Keywords: Approximate Nash Equilibria, CORR 2010, Education, Nash Equilibria, Nash Equilibrium