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NotesECN741-page35

# NotesECN741-page35 - ECN 741 Public Economics Fall 2008 A...

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ECN 741: Public Economics Fall 2008 A BNE is a strategy α * : D -→ A ( α t is θ t - measurable) such that T X t =1 β t - 1 π ( θ T ) u ( g c t ( α * t ( θ T ) , μ * )) - v g c t ( α * t ( θ T ) , μ * ) θ t T X t =1 β t - 1 π ( θ T ) u ( g c t ( α 0 t ( θ T ) , μ * )) - v g c t ( α 0 t ( θ T ) , μ * ) θ t for all α 0 : D -→ A ( α 0 t is θ t - measurable) and μ * ( a ) = { θ T | α ( θ T )= a } π ( θ T ) . An allocation is implementable if there exist a mechanism ( A, g c , g y ) and a BNE α * such that ( c t ( θ T ) , y t ( θ T )) = g t ( α * ( θ T ) , μ * ) A mechanism is a direct mechanism if A = Θ T . A strategy α is truth-full if α t ( θ T ) = θ t for all θ T Θ T . An allocation is truthfully implementable if there exists a BNE of a direct mechanism, i.e., if T X t =1 β t - 1 π ( θ T ) u ( g c t ( θ T , μ * )) - v g y t ( θ T , μ * ) θ t T X t =1 β t - 1 π ( θ T ) u ( g c t ( α 0 t ( θ T ) , μ * )) - v g y t ( α 0 t ( θ T ) , μ * ) θ t for all α 0 : D -→ Θ T ( α 0 t is θ t - measurable) μ * ( a ) = { θ T | θ T = a } π ( θ T ) = π ( a ) . And
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