In the dynamic programming problem (example 2.32) subject to xt+1 G(xt) t = 0, 1, 2, .
Question:
subject to xt+1 G(xt)
t = 0, 1, 2, . . . , x0 X given
Assume that
¢ f is bounded, continuous and strictly concave on X Ã X.
¢ G(x) is nonempty, compact-valued, convex-valued, and continuous for every x 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
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