STRATEGY-PROOF MULTINARY GROUP IDENTIFICATION - Gopakumar Achuthankutty Indira Gandhi Institute of Development Research, Mumbai

A CIF f : Gn×n→ Gn satisfies strategy-proofness if for all P ∈ Gn×n, for all i ∈ N, and for all P′ ∈ Gni , either f (P) = f (P′i , PN\i) or f (P)Q ′i f (Pi , PN\i). [...] This means that for all P ∈ Gn×n, for all i ∈ N, and for all P′ ∈ Gn×n, f (P) , f (P′i i , PN\i) implies f (P)QPi f (P′i , PN\i). [...] For j ∈ N, define n the column-j CIF φ f ,j : B j → G associated to f as follows: for all P ∈ Gn×n and for all i ∈ N, f ,j f φi (B P,j) = fi(P) if i = j and φi (B P,j) = 0 if i , j. [...] We show that f is strategy-proof ,i.e., for all P ∈ Gn×n, for all i ∈ N, and for all P′i ∈ Gn×n, 8 f (P) , f (P′i , PN\i) implies f (P)Q P i f (P ′ i , PN\i). [...] Since f j(P) , f j(P′i , PN\i) for all j ∈ Ñ f , we have φ f ,j(BP,j) , φ f ,j(B (Pi ,PN\i),j) and since φ f ,j is strategy-proof, this means that φ f ,j(BP,j)QB P,j φ f ,j(B(P ′ i ,PN\i),j i ), thereby implying that f P f ,j P,j f ,j ′ (P′,P ),j j( ) = φj (B P,j) , Bij = Pij implies that f j(P ′, P ) = φ (B(Pi ,PN\i),j) , B i N\ii N\i j ij = Pij.