Polynomial-time computation of Nash equilibria in two-player non-zero-sum and multiplayer games

Determine whether a polynomial-time algorithm exists for computing a Nash equilibrium in two-player non-zero-sum games and in multiplayer games, thereby confirming or refuting the conjecture that no efficient (polynomial-time) algorithm exists for these classes.

Background

The paper contrasts the tractability of computing Nash equilibria in two-player zero-sum normal-form games—where polynomial-time algorithms are known—with the computational hardness in two-player non-zero-sum and multiplayer settings. It notes PPAD-completeness for the latter, and explicitly mentions the widely held conjecture that no polynomial-time algorithm exists for computing Nash equilibria in these cases.

Resolving this conjecture would clarify the fundamental algorithmic limits of equilibrium computation beyond zero-sum games and has broad implications for game-theoretic analysis and algorithm design across economics and computer science.