A Bridge between Polynomial Optimization and Games with Imperfect Recall

Hugo Gimbert (1, 2) , Soumyajit Paul (1) , B. Srivathsan (3)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 CNRS - Centre National de la Recherche Scientifique
3 Chennai Mathematical Institute [Inde]

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.

Mots clés: Non-cooperative game theory; extensive form games; complexity; Bridge; first order theory of reals; polynomial optimization

Domaines: Informatique [cs]; Informatique et théorie des jeux [cs.GT]; Logique en informatique [cs.LO]

Hugo Gimbert, Soumyajit Paul, B. Srivathsan. A Bridge between Polynomial Optimization and Games with Imperfect Recall. 2020. ⟨hal-02488256v1⟩