是Eric Rasmusen写的Games and information: an introduction to game theory的13章里面的一道习题。
那个第二问和第三问问的是什么呀？什么是puts on different values of Z？

13.4. An Auction with Stupid Bidders (hard)
Smith’s value for an object has a private component equal to 1 and another component Z that
is common with Jones and Brown. Jones’s and Brown’s private components both equal zero.
Each bidder estimates Z independently. Bidder i’s estimate is either xi above the true value or xi
below, with equal probability. Jones and Brown are naive and always bid their value estimates.
The auction is ascending. Smith knows all three values of xi , but not whether his estimate is too
high or too low.
(a) If xSmith = 0, what is Smith’s dominant strategy if his estimate of Z is 20?
(b) If xi = 8 for all bidders and Smith estimates that Z = 20, what are the probabilities that
he puts on different possible values of Z?
(c) If xi = 8 for Jones and Brown but xSmith = 0, and Smith knows that Z = 12 with certainty,
what are the probabilities he puts on the different combinations of bids by Jones and Brown?
(d) Why is 9 a better upper limit on bids for Smith than 21, if his estimate of Z is 20, and
xi = 8 for all three bidders?

大牛指教阿！！！