In the dynamic programming problem (example 2.32) subject to xt+1 G(xt) t = 0, 1, 2, . . . , x0 X given Assume that

In the dynamic programming problem (example 2.32)

subject to xt+1 ˆˆ G(xt)
t = 0, 1, 2, . . . , x0 ˆˆ X given
Assume that
€¢ f is bounded, continuous and strictly concave on X × X.
€¢ G(x) is nonempty, compact-valued, convex-valued, and continuous for every x ˆˆ X
€¢ 0 ‰¤ β We have previously shown (exercise 2.124) that an optimal policy exists under these assumptions. Show also that
1. The value function v is strictly concave
2. The optimal policy is unique

EB'f(xi, X+1) max 1=0