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Consider a sealed-bid auction where the bid for the object is either a or b where O a < b and 2a > b, The higher bidder gets the object at the pace of Ifthe two bids are identical, winner is decided by a toss of an umbiased coin. Suppose there are nvo types of possible buyers, those who value the obJect at b units (Type H) and those who value it at a units (Type L). Assume that a bidder makes the bid independently Of the Other bidder. a) By considering the gain each bidder will receive on making his bid, find all Nash equilibrium points m pure strategies for this auction. IVIuch, if any, of these NEPs produce the fairest outcome to both players? Note: to obtain the strategic form for the game: the payoff (or gam) for each player can be computed as gain valuation Of Object expected payment or O in case the player does not Win the Object. each piayer belongs to the Ope space (H, L} _ each player has Strategy set (a the strategic-form should pssi&ie types that each player can assume For ccmn", players Ope is I)pc (L, H), Piaye 's type is L, and Player 2 's Ope ts H suppose Type (L, H), the possible payoffs can be obtatned by constdertng L bids a, H bids a: L gains a H gams b L bids a. H bids b: L gains O, H gains b Assuming that I q and = q and that the bidders report true valuations, what can the seller expect to receive under thig auction? (Hint: thc zvecrcd value can be o brained by considering thefcnmvtng scenarios: t. Both player are H, u. Exactly player Ope H: iii. Both player are L c) Compare the expected selling price Of this auction With the first best outcome mechanism and the Vickrey auction for various q values where O s q s (Hint: comprc the expected selling price of this aucncn with thcfirsr best outcome mechanism ara Vickrey auction, you n.@ assume a 3 am' b 4, the lower bid value f.' 3 units and h.'gh btd value is 4 units.)