AGT tutorial exercise: week 3
Consider the following mixed‐format simultaneous posted‐offer auction with n bidders. A
bidder i can pass or submit a bid bi ≥ 0. Every bidder who bids pays participation cost c > 0
at the time of bidding. The object goes to the highest bidder. In case of more individuals
giving the same bid, the object goes to the bidder with the highest valuation (assume
valuations v1 > v2 > ... > vn ). The winner pays the k‐th highest bid, in addition to the cost c of
its bid, and receives the object. The other bidders pay only the cost c (even if they bid 0), but
pay no cost if they pass. If all bidders pass, none gets the object.
a. Let k=2. When can player 2 win the object in the Nash equilibrium?
b. Let k=1. When can we find a Nash equilibrium in pure strategies?
c. Can you prove revenue equivalence for auctions with k=1 and k=2?