Exam 13: Committing and Uncommitting

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When a sophisticate binds himself to a path of action using a commitment mechanism, at every period tt , he sees that he is better off with the commitment mechanism than without.

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A sophisticate solves the inter-temporal model recursively, while a naiff solves the intertemporal problem simultaneously from the point of view of the first period.

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A sophisticate cannot be made worse-off by committing.

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Why is a naif unwilling to pay for a commitment mechanism?

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Scenarios in which rewards are experienced in the same time period as the action to acquire the reward are called,

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Consider the example given on pages 3-12 and 3-13. Suppose kv=kc=1k_{v}=k_{c}=1 , that is both costs and rewards are immediate. Let the remaining parameters be unchanged, so that vt=v_{t}= {8,20,0},ct={0,9,1},β=12,δ=1\{8,20,0\}, c_{t}=\{0,9,1\}, \beta=\frac{1}{2}, \delta=1 . In this setting, the sophisticate obeys the dominance property.

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An assumption that is implicitly built in to the fully additive inter-temporal model is

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The difference in timing between rewards and costs explain the violation of the dominance property by naifs and sophisticates.

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A partially naïf individual believes βδ\beta \neq \delta , but β=β^\beta=\hat{\beta} . If β=12\beta=\frac{1}{2} , which of the following could be possible values of β^\hat{\beta} ?

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