In Benjamin Edelman, Michael Ostrovsky, and Michael Schwarz(2007), there's a hand-waving argument to justify their setting as a game of complete information:
we assume that all values are common knowledge: over time, advertisers are likely to learn all relevant information about each other's values.
My question is, to what degree, this reasoning can be justified?
My feeling is that, for an auction with an infinite type space and at least one bidder having a partition of infinite cells, it is wrong(see Geanakoplos and Polemarchakis (1982)). To proceed, it seems to me, one needs to represent a bidder's bidding strategy as a function measurable with respect to her own type, and history records of bidding, which seems to be quite complicated.