In the second price auction version of three bidder one seller problem, suppose that the seller sets a low reserve and the bidders are almost convinced that the preferences are as we described them v1 > v2 > v3. However suppose that bidders 1 and 2 are not quite sure of bidder 3's motivation. In particular, suppose that both of them assign a small probability (say 1/100) to the possibility that 3 is a 'religious' bidder who simply wants to submit the highest bid he can win or lose in order to show his devotion to the product. The second complication is that they just aren't sure how much money a religious bidder might have. Suppose that both of them think that a religious bidder has some amount of money m which is uniformly distributed on the interval [0, v4] where v4 > v1. They don't think it is very likely that 3 is religious, but if he is, they expect him to bid whatever he has. Write down the expected payoffs of bidders 1 and 2 when they expect religious 3 to bid uniformly on the interval [0, v4] and the sensible 3 to bid a best reply to what they are doing. Are there any inefficient equilibrium outcomes in which 1 doesn't get the good even when 3 is sensible instead of religious. Can you see any advantage to 3 of cultivating an image as a religious bidder?