Micro- Notes on Correlation The foregoing discussion leaves open the issue of correlation vs. independence of signals. I will merely point out the differences between these two cases in a limiting case: you should consult Myerson,s 1981 paper, or Cremer and McLean's paper, for more on the topic Let us consider a two-bidder first-price auction with private values and perfectly correlated als: that is, Pr Thus, as soon as a bidder learns her signal, she also learns her opponent's signal; for all practical purposes, at the interim stage the players are actually engaged in a game with complete information It should be clear that the only equilibrium in the game where both signals equal some sE0, 1] is for both players to bid exactly s, i.e. their valuation(if the winning bidder bids more than her opponent, she gains by reducing her bid; if both are bidding a <s, then either one can gain by raising her bid slightly above a). Thus, there is no shading, and the seller is able to extract the whole surplus from the players the stochastic structure of the signals matter hy case, this simple example emphasizes that This turns out to be a general result. InMicro-Notes on Correlation The foregoing discussion leaves open the issue of correlation vs. independence of signals. I will merely point out the differences between these two cases in a limiting case: you should consult Myerson’s 1981 paper, or Cremer and McLean’s paper, for more on the topic. Let us consider a two-bidder first-price auction with private values and perfectly correlated signals: that is, Pr{s1 = s2} = 1. Thus, as soon as a bidder learns her signal, she also learns her opponent’s signal; for all practical purposes, at the interim stage the players are actually engaged in a game with complete information. It should be clear that the only equilibrium in the game where both signals equal some s ∈ [0, 1] is for both players to bid exactly s, i.e. their valuation (if the winning bidder bids more than her opponent, she gains by reducing her bid; if both are bidding a < s, then either one can gain by raising her bid slightly above a). Thus, there is no shading, and the seller is able to extract the whole surplus from the players. This turns out to be a general result. In any case, this simple example emphasizes that the stochastic structure of the signals matters. 9