(a) In a third price sealed bid auction, there is an item for sale and n bidders (players) that wish to obtain the item, each bidder i having their own valuation vi for the item. All bidders simultaneously submit sealed bids, so that no bidder knows the bid of any other participant. The highest bidder wins the item and pays the price of the third highest bid. The payoff of the bidder who obtains the item is their valuation minus the price they paid, and the rest of the bidders' payoffs are 0. Suppose, furthermore, that the players' valuations for the item satisfy: v1>v2>>vn>0. Let (b1,b2,,bn) be an action profile where player i bids bi=vi, i.e. every player bids truthfully. a1) (3 marks) Is this profile a Nash equilibrium? a2) (10 marks) Justify your answer to a1). b) We are given three sellers (a,b,c) each offering a distinct house for sale. We also have three buyers x,y,z. The valuations of the buyers for the houses are as follows: b1) (9 marks) Run the bipartite graph auction procedure and state what the prices are at the end of each round. b2) ( 3 marks) State what is the eventual set of market-clearing prices