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View all- Babichenko YRubinstein A(2020)Communication complexity of approximate Nash equilibriaGames and Economic Behavior10.1016/j.geb.2020.07.005Online publication date: Aug-2020
Simple Approximate Equilibria in Games with Many Players
Pages 681 - 691
Abstract
We consider ε-equilibria notions for a constant value of ε in n-player m-action games, where m is a constant. We focus on the following question: What is the largest grid size over the mixed strategies such that ε-equilibrium is guaranteed to exist over this grid.
For Nash equilibrium, we prove that constant grid size (that depends on ε and m, but not on n) is sufficient to guarantee the existence of a weak approximate equilibrium. This result implies a polynomial (in the input) algorithm for a weak approximate equilibrium.
For approximate Nash equilibrium we introduce a closely related question and prove its equivalence to the well-known Beck-Fiala conjecture from discrepancy theory. To the best of our knowledge, this is the first result that introduces a connection between game theory and discrepancy theory.
For a correlated equilibrium, we prove a O(1 over log n) lower-bound on the grid size, which matches the known upper bound of Ω(1 over log n). Our result implies an Ω(log n) lower bound on the rate of convergence of any dynamic to approximate correlated (and coarse correlated) equilibrium. Again, this lower bound matches the O(log n) upper bound that is achieved by regret minimizing algorithms.
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References
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Index Terms
- Simple Approximate Equilibria in Games with Many Players
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Published In
June 2017
740 pages
ISBN:9781450345279
DOI:10.1145/3033274
- General Chair:
- Constantinos Daskalakis,
- Program Chairs:
- Moshe Babaioff,
- Hervé Moulin
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Published: 20 June 2017
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View all- Babichenko YRubinstein A(2020)Communication complexity of approximate Nash equilibriaGames and Economic Behavior10.1016/j.geb.2020.07.005Online publication date: Aug-2020
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