Search papers, labs, and topics across Lattice.
This paper introduces an asymmetric projected gradient descent-best response iteration for finding Nash equilibria in two-player constrained games where one player only has access to the other's best-response map. The authors prove global linear convergence of the proposed method under regularity conditions when the best-response map is exact. They also show that with an inexact best-response map having a uniform error bound of $\varepsilon$, the iterates converge to an $O(\varepsilon)$ neighborhood of the true Nash equilibrium.
You can provably find Nash equilibria even when one player only knows the *reaction* of the other, not their full objective.
Nash equilibria provide a principled framework for modeling interactions in multi-agent decision-making and control. However, many equilibrium-seeking methods implicitly assume that each agent has access to the other agents'objectives and constraints, an assumption that is often unrealistic in practice. This letter studies a class of asymmetric-information two-player constrained games with decoupled feasible sets, in which Player 1 knows its own objective and constraints while Player 2 is available only through a best-response map. For this class of games, we propose an asymmetric projected gradient descent-best response iteration that does not require full mutual knowledge of both players'optimization problems. Under suitable regularity conditions, we establish the existence and uniqueness of the Nash equilibrium and prove global linear convergence of the proposed iteration when the best-response map is exact. Recognizing that best-response maps are often learned or estimated, we further analyze the inexact case and show that, when the approximation error is uniformly bounded by $\varepsilon$, the iterates enter an explicit $O(\varepsilon)$ neighborhood of the true Nash equilibrium. Numerical results on a benchmark game corroborate the predicted convergence behavior and error scaling.
