Talk:Revenue equivalence

Misstatement of the theorem
To say the theorem is about "...the same social choice function..." grossly misstates the theorem. The 1st and 2nd price auctions are clearly not the same SCF. The theorem says "if two Bayesian implementable SCF's are the same in the interim stage for any agent, then the total expected transfers are the same (under their respective Bayesian equilibria)." There are also missing key assumptions: types need to be independently drawn, the expecting probability of winning for any agent has to be the same across auctions, and an lowest-type agent agent must have the same expected utility across auctions. Mct mht (talk) 11:56, 29 April 2013 (UTC)

The article is very wrong
As of 2015 February 12, the article says:

"The buyer's types, or valuations of the object, are independent identically distributed random variables."

"Theorem: For any two Bayesian incentive compatible auctions, if under their respective Bayesian Nash equilibria where all players bid their type, ..."

Taken together, the above two statements imply that the theorem requires that all players bid their type, i.e., their value. This is incorrect. The theorem holds even when players do not bid their value.

The article also fails to mention that the expected payment as a function of the player's value will be the same in any qualifying auction. Even though this point is not stated, the point is used later in the article, in the section "Using Revenue Equivalence to Predict Bidding Functions".

For a correct statement of the theorem, see:

http://www.econport.org/econport/request?page=man_auctions_revequiv

--Mpb2 (talk) 19:58, 2 February 2015 (UTC)