A Manifold of Polynomial Time Solvable Bimatrix Games

This paper identifies a manifold in the space of bimatrix games which contains games that are strategically equivalent to rank-1 games through a positive affine transformation. It also presents an algorithm that can compute, in polynomial time, one such rank-1 game which is strategically equivalent to the original game. Through this approach, we substantially expand the class of games that are solvable in polynomial time. It is hoped that this approach can be further developed in conjunction with other notions of strategic equivalence to compute exact or approximate Nash equilibria in a wide variety of bimatrix games.

💡 Research Summary

The paper “A Manifold of Polynomial Time Solvable Bimatrix Games” investigates a broad class of two‑player finite games that can be solved in polynomial time by exploiting a structural relationship with rank‑1 games. A bimatrix game is specified by two payoff matrices A and B; the sum C = A + B determines the “rank” of the game. Rank‑1 games—those for which C has rank one—are known to admit polynomial‑time algorithms for computing Nash equilibria (e.g., via the methods of Adsul et al.