Competitive Equilibrium (Stokey-Lucas)

An allocation [(xi0), (yj0)] together with a continuous linear functional φ: S → R is a competitive equilibrium if

(E1) [(xi0), (yj0)] is feasible;
(E2) for each i, x ∈ Xi and φ(x) ≤ φ(xi0) implies ui(x) ≤ ui(xi0); and
(E3) for each j, y ∈ Yj implies φ(y) ≤ φ(yj0).

Stokey, Lucas "Recursive Methods in Economic Dynamics" p.453