General convergence of Nash-equilibrium computation

Characterize convergence guarantees for numerical methods that compute feedback Nash equilibria in general nonzero-sum stochastic differential games, beyond the local, equilibrium-dependent conditions established for the sequential policy-iteration method.

Background

The paper situates policy iteration for stochastic differential games within a broader numerical-computation problem. Unlike single-player optimization, coupled nonzero-sum equilibrium conditions form a fixed-point problem and do not generally inherit the monotonicity properties used to prove convergence of classical policy-iteration methods.

The authors emphasize that multiple stabilizing feedback Nash equilibria may exist, even in deterministic special cases. Consequently, global convergence to a distinguished equilibrium cannot generally be expected without additional assumptions, and the convergence behavior depends on the selected equilibrium. The paper resolves a narrower problem by deriving local convergence criteria for its sequential policy-iteration scheme, leaving convergence for the general computation of Nash equilibria open.