Deligkas, Argyrios and Fearnley, John and Hollender, Alexandros and Melissourgos, Themistoklis (2022) Pure-Circuit: Strong Inapproximability for PPAD. In: FOCS 2022: 63rd IEEE Symposium on Foundations of Computer Science, 2022-10-31 - 2022-11-03, Denver, Colorado.
Deligkas, Argyrios and Fearnley, John and Hollender, Alexandros and Melissourgos, Themistoklis (2022) Pure-Circuit: Strong Inapproximability for PPAD. In: FOCS 2022: 63rd IEEE Symposium on Foundations of Computer Science, 2022-10-31 - 2022-11-03, Denver, Colorado.
Deligkas, Argyrios and Fearnley, John and Hollender, Alexandros and Melissourgos, Themistoklis (2022) Pure-Circuit: Strong Inapproximability for PPAD. In: FOCS 2022: 63rd IEEE Symposium on Foundations of Computer Science, 2022-10-31 - 2022-11-03, Denver, Colorado.
Abstract
The current state-of-the-art methods for showing inapproximability in PPAD arise from the ε-Generalized-Circuit (ε-GCircuit) problem. Rubinstein (2018) showed that there exists a small unknown constant ε for which ε-GCircuit is PPAD-hard, and subsequent work has shown hardness results for other problems in PPAD by using ε-GCircuit as an intermediate problem. We introduce Pure-Circuit, a new intermediate problem for PPAD, which can be thought of as ε-GCircuit pushed to the limit as ε→1, and we show that the problem is PPAD-complete. We then prove that ε-GCircuit is PPAD-hard for all ε<0.1 by a reduction from Pure-Circuit, and thus strengthen all prior work that has used GCircuit as an intermediate problem from the existential-constant regime to the large-constant regime. We show that stronger inapproximability results can be derived by reducing directly from Pure-Circuit. In particular, we prove tight inapproximability results for computing ε-well-supported Nash equilibria in two-action polymatrix games, as well as for finding approximate equilibria in threshold games.
Item Type: | Conference or Workshop Item (Paper) |
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Additional Information: | Published proceedings: _not provided_ |
Uncontrolled Keywords: | TFNP; PPAD; approximation; Nash equilibrium; polymatrix games; generalized circuit |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Computer Science and Electronic Engineering, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 04 Oct 2022 13:07 |
Last Modified: | 19 Sep 2024 20:55 |
URI: | http://repository.essex.ac.uk/id/eprint/33602 |
Available files
Filename: Pure-Circuit - Strong Inapproximability for PPAD.pdf