Read a couple of pages..... don't understand a thing. The guy must be a genius.
Definition 20. fN is symmetric if its value is equal under any permutation of its
arguments. fN is affiliated if for all θN , θ0
N :
fN (θN ∨ θ
0
N )fN (θN ∧ θ
0
N ) ≥ fN (θN )fN (θ
0
N ) (8)
where ∨ is the component-wise maximum and ∧ the component-wise minimum.
Definition 21. (G, SN ) is optimal among ex post auctions if it maximizes π(G, SN )
subject to the constraints:
1. Ex post incentive compatibility. For all i, θi
, θ0
i
, θ−i:
θiy
G,SN
i
(θi
, θ−i) − t
G,SN
i
(θi
, θ−i) ≥ θiy
G,SN
i
(θ
0
i
, θ−i) − t
G,SN
i
(θ
0
i
, θ−i) (9)
2. Ex post individual rationality. For all i, θi
, θ−i:
θiy
G,SN
i
(θi
, θ−i) − t
G,SN
i
(θi
, θ−i) ≥ 0 (10)
