Consider the following simple model $of$ a common values auction. Ilsa Faust and Benji

Dunn participate $inan$ anonymous auction $on$ the dark net $(theydo$ not know the

identity $or$ location $of$ auction participants$).$ They $do$ know that the Syndicate $(totally$

evil and profit$-$oriented$)$ sells a stash $of$ allegedly super secret documents describing

extra$-$terrestrial super$-$pooper advanced technology. Each buyer $(Ilsa$ and Benji, that $is)$

obtain a private signal about the value $of$ the stash. The signal can $be$ either high $(H)L.If$ both obtain signal $H,$ the object $is$ worth $1(itisa$

genuine stash $of$ documents related $to$ advanced extraterrestrial technology$)$;

otherwise, $itis$ worth $0(totally$ fake$).$

$(a)$ What $is$ the expected value $of$ the stash $to$ a buyer who sees signal $L?To$ a buyer

who sees signal $H?$

$(b)$ What $is$ the sellers' expected revenue from the auction?

$(c)$ Suppose buyers bid their expected value computed $in$ part $(a)-$ according $to$ the

signal they see. Show that they earn negative profit conditional $on$ observing signal

$H-an$ example $of$ the winner's curse.

$(d)$ Would were analysis change $if$ buyer signals are statistically dependent, say,

positively correlate with each other?