The following example is based on Acemoglu and Özdağlar. There are two bidders participating in a first-price sealed-bid auction for an object that has either high quality (value V) or low quality (value 0) to both of them. Each bidder receives a signal that can be either high or low, with probability 1/2. The signal is related to the true value as follows: If at least one bidder receives a low signal, then the true value is 0. If both receive a high signal, then the true value is V. This game has no SBNE in pure-strategies. 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: The other bidder bids B2 < B1. Then, his expected gain is 1/2 (the probability that bidder 2 has a low signal) times −B2 (since in that case he wins a worthless item and pays b2(high)), plus 1/2 (the probability that bidder 2 has a high signal) times 0 (since in that case he loses the item). The total expected gain is −B2/2 which is worse than 0, so it cannot be a best response. The other bidder bids B2 = B1. Then, his expected gain is 1/2 times −B2, plus 1/2 times 1/2 times [V− B2] (since in that case, he wins the item with probability 1/2). The total expected gain is (V − 3 B2)/4. The bidder b2 bids B2 > B1. Then, his expected gain is 1/2 times −B2, plus 1/2 times [V− B2] (since in that case, he wins the item with probability 1). The total expected gain is (2 V − 4 B2)/4. The latter expression is positive only when B2 < V/2. But in that case, the expression in #3 is larger than the expression in #2: it is always better to bid slightly more than the other bidder. This means that there is no symmetric equilibrium. This result is in contrast to the private-value case, where there is always a SBNE