A hypergradient-free social-gradient flow is proven to be a descent direction for the planner's objective and converges to the unique socially optimal incentive when social cost depends on agents' joint actions.
Geometric Convergence of Gradient Play Algorithms for Distributed Nash Equilibrium Seeking
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Incentive Design without Hypergradients: A Social-Gradient Method
A hypergradient-free social-gradient flow is proven to be a descent direction for the planner's objective and converges to the unique socially optimal incentive when social cost depends on agents' joint actions.