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Optimal Strategy Revision in Population Games via Finite-State Mean Field Games

How the design of agents' strategy-revision protocols in population games can be derived by casting evolutionary dynamics as a finite-state mean field game and solving its coupled forward Fokker-Planck and backward Hamilton-Jacobi equations. How the resulting payoff-maximizing revision satisfies positive correlation and Nash stationarity, guaranteeing convergence to a Nash equilibrium and recovering existing evolutionary-dynamics models as special cases.