Decision Theory Meets Linear Optimization Beyond Computation

The utility function u is then extended to a utility function G(u) on G(A)×Θ by assigning each pair (λ, θ) the expectation of the random variable uθ under the measure λ, i.e. Eλ [ uθ ] . Every pure action a ∈ A then can uniquely be identified with the Dirac-measure δa ∈ G(A) and we have u(a, θ) = G(u)(δa, θ) for all (a, θ) ∈ A × Θ. Further, also (1) can easily be extended to randomized actions by defining, for every λ ∈ G(A) fixed, G(u)λ(θ) := G(u)(λ, θ) for all θ ∈ Θ.