https://www.econjobrumors.com/topic/explainbellmanequations
Explain Bellman equations

I’m confused by this too. The contraction theorem makes sense, especially when thinking about contractions from Rn to Rn. But why is the Bellman operator a contraction, intuitively? Yeah yeah you may prove that it’s a contraction by showing Blackwell’s conditions are satisfies, but surprisingly little insight is achieved with this (at least for me).

I’m confused by this too. The contraction theorem makes sense, especially when thinking about contractions from Rn to Rn. But why is the Bellman operator a contraction, intuitively? Yeah yeah you may prove that it’s a contraction by showing Blackwell’s conditions are satisfies, but surprisingly little insight is achieved with this (at least for me).
Whwhat?

I’m confused by this too. The contraction theorem makes sense, especially when thinking about contractions from Rn to Rn. But why is the Bellman operator a contraction, intuitively? Yeah yeah you may prove that it’s a contraction by showing Blackwell’s conditions are satisfies, but surprisingly little insight is achieved with this (at least for me).
V_{n+1}(x) = max{x' in Gamma(x)} { F(x,x') + b V_n(x') }
W_{n+1}(x) = max{x' in Gamma(x)} { F(x,x') + b W_n(x') }Intuitively, d(V_{n+1},W_{n+1}) < d(V_n, W_n) because V_{n+1} (W_{n+1}) is kind of like a weighted average between F(x,x') and V_n (W_n) (recall that 0 < b < 1  the "discounting" assumption in Blackwell's sufficient conditions). Because the term F(x,x') is "the same" in both cases, the weighted averages are closer than the original functions V_n, W_n are to each other.
"The same" is in quotes because of course x' will be different in the two cases. This is why you need another condition. One such condition is the monotonicity assumption of Blackwell.

I’m confused by this too. The contraction theorem makes sense, especially when thinking about contractions from Rn to Rn. But why is the Bellman operator a contraction, intuitively? Yeah yeah you may prove that it’s a contraction by showing Blackwell’s conditions are satisfies, but surprisingly little insight is achieved with this (at least for me).
Otherwise no stationary solution.