A Bridge between Polynomial Optimization and Games with Imperfect Recall

• Main Authors: Gimbert, Hugo, Paul, Soumyajit, Srivathsan, B
• Format: Journal Article
• Language: English
• Published: 23-02-2020
• Subjects: Computer Science - Computer Science and Game Theory; Computer Science - Logic in Computer Science
• DOI: 10.48550/arxiv.2002.09941

We provide several positive and negative complexity results for solving games
with imperfect recall. Using a one-to-one correspondence between these games on
one side and multivariate polynomials on the other side, we show that solving
games with imperfect recall is as hard as solving certain problems of the first
order theory of reals. We establish square root sum hardness even for the
specific class of A-loss games. On the positive side, we find restrictions on
games and strategies motivated by Bridge bidding that give polynomial-time
complexity.