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Tom's second April 6 edits of dyn_stack.md lecture
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lectures/dyn_stack.md

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@@ -1117,6 +1117,13 @@ axes[2].set(title=r'$v(y_{t})$ and $w(\hat x_t)$', xlabel='t')
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plt.tight_layout()
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plt.show()
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```
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The figure above shows
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* in the third panel that for $t \geq 1$ the **reborn at $t$** Stackelberg leader's's value $w(\hat x_0)$ exceeds the continuation value $v(y_t)$ of the time $0$ Stackelberg leader
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* in the first panel that for $t \geq 1$ the **reborn at $t$** Stackelberg leader wants to reduce his output below that prescribed by the time $0$ Stackelberg leader
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* in the second panel that for $t \geq 1$ the **reborn at $t$** Stackelberg leader wants to increase the output of the follower firm 2 below that prescribed by the time $0$ Stackelberg leader
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Taken together, these outcomes express the time inconsistency of the original time $0$ Stackelberg leaders's plan.
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## Recursive Formulation of Follower's Problem
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