PROOF: Suppose that there was such an equilibrium "b". This is a function from a signal to a bid, i.e., a player with signal "x" bids "b"("x"). Clearly "b"(low)=0, since a player with low signal knows with certainty that the true value is 0 and does not want to pay anything for it. Also, "b"(high) ≤ V, otherwise there will be no gain in participation. Suppose bidder 1 has "b1"(high)=B1 > 0. We are searching the best-response for bidder 2, "b2"(high)=B2. There are several cases: