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Recent developments in domains such as non-local games, quantum interactive proofs, and quantum generative adversarial networks have renewed interest in quantum game theory and, specifically, quantum zero-sum games. Central to classical game theory is the efficient algorithmic computation of Nash equilibria, which represent optimal strategies for both players. In 2008, Jain and Watrous proposed the first classical algorithm for computing equilibria in quantum zerosum games using the Matrix Multiplicative Weight Updates (MMWU) method to achieve a convergence rate of O(d/ε2) iterations to ε-Nash equilibria in the 4d-dimensional spectraplex. In this work, we propose a hierarchy of quantum optimization algorithms that generalize MMWU via an extra-gradient mechanism. Notably, within this proposed hierarchy, we introduce the Optimistic Matrix Multiplicative Weights Update (OMMWU) algorithm and establish its average-iterate convergence complexity as O(d/ε) iterations to ε-Nash equilibria. This quadratic speed-up relative to Jain and Watrous’ original algorithm sets a new benchmark for computing ε-Nash equilibria in quantum zero-sum games.
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Nash Equilibrium in Discontinuous Games
We review the discontinuous games literature, with a sharp focus on conditions that ensure the existence of pure and mixed strategy Nash equilibria in strategic form games and of Bayes-Nash equilibria in Bayesian games.
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- Award ID(s):
- 1724747
- PAR ID:
- 10309070
- Date Published:
- Journal Name:
- Annual Review of Economics
- Volume:
- 12
- Issue:
- 1
- ISSN:
- 1941-1383
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1146/annurev-economics-082019-111720
