NotesECN741-page34

# NotesECN741-page34 - ³ θ T | π θ T> ´ Deﬁne...

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ECN 741: Public Economics Fall 2008 the ones that satisfy the following incentive compatibility constraints X θ - n π ( θ - n ) ± u ( c n ( θ n - n )) + v ± y n ( θ n - n ) θ n ²² X θ - n π ( θ - n ) ± u ( c n ( θ 0 - n )) + v ± y n ( θ 0 - n ) θ n ²² n,θ n 0 Θ . We are going to primarily focus on environment with unit measure of agents. Environment with inﬁnite number of agents Consider the same environment as before (for general T < ) except that now there are unit mass of agents. Nature makes a draw θ T = ( θ 1 ,...,θ t ) Θ T = Θ × ··· × Θ for each agent. The θ T draws are i.i.d across agents. Let π ( · ) is probability density function over Θ T draws. There is no aggregate uncertainty, therefore π ( θ T ) is also the mass of people who have the draw θ T . Let D
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Unformatted text preview: ³ θ T | π ( θ T ) > ´ . Deﬁne allocation as θ t-measurable functions c t : D-→ R T + y t : D-→ R T + Allocation is feasible if X Θ ∈ D T X t =1 R-t c t ( θ T ) π ( θ T ) ≤ X Θ ∈ D T X t =1 R-t y t ( θ T ) π ( θ T ) Deﬁne a mechanism as set of actions A ⊂ Q T t =1 X t and outcome functions g : A × Δ( A )-→ R 2 T + and g t ( a,μ ) = g t ( a ,μ ) if a t = a t and X ( a t +1 ,...,a T ) μ (¯ a t ,a t +1 ,...,a T ) = X ( a t +1 ,...,a T ) μ (¯ a t ,a t +1 ,...,a T ) ∀ ¯ a t in which μ,μ ∈ Δ( A ) are measure of actions chosen. 34...
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## This note was uploaded on 12/10/2011 for the course MAT 121 taught by Professor Wong during the Fall '10 term at SUNY Stony Brook.

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