Third-Price Sealed-Bid Auction In the auction of Sect. 6.5.1, assume that there are at least three..

Third-Price Sealed-Bid Auction

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In the auction of Sect. 6.5.1, assume that there are at
least three bidders and that the highest bidder wins and pays the third highest
bid.

(a) Show that for any player i bidding vi weakly dominates
any lower bid but does not weakly dominate any higher bid.

(b) Show that the strategy combination in which each player
i bids his true valuation vi is in general not a Nash equilibrium.

(c) Find some Nash equilibria of this game.