Mean Field Games without Rational Expectations

The paper explicitly formulates the agent’s problem under low-dimensional coupling and non-rational expectations as a finite-dimensional HJB in (x,z,p) with generator A_α = α·∇_x + νΔ_x, plus βΔ_z and an exogenous perceived price operator Â_p, see its equation (6.4). The candidate solution derives exactly this HJB via dynamic programming and Itô’s formula with the same state, operators, terminal condition, and feedback characterization. The only mild specialization is the candidate’s explicit independence assumption for the price and aggregate shocks, which is one of the paper’s simplest benchmark specifications. The conclusions align: the agent’s optimization step does not require an infinite-dimensional Master equation under non-rational expectations.