(Third-price auction) Consider a third-price sealed-bid auction, which differs from a first- and… 1 answer below »

(Third-price auction) Consider a third-price sealed-bid auction, which differs from a first- and a second-price auction only in that the winner (the person who submits the highest bid) pays the third highest price. (Assume that there are at least three bidders.)

a. Show that for any player i the bid of vi weakly dominates any lower bid, but does not weakly dominate any higher bid. (To show the latter, for any bid bi > vi find bids for the other players such that player i is better off bidding bi than bidding vi.)

b. Show that the action profile in which each player bids her valuation is not a Nash equilibrium.

c. Find a Nash equilibrium. (There are ones in which every player submits the same bid.)