An object is to be assigned to a player in the set{1,2, … , ??}in exchange for a payment…. 1 answer below »
An object is to be assigned to a player in the set{1,2, … , ??}in exchange for a payment…. 1 answer below » | savvyessaywriters.org
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An object is to be assigned to a player in the set{1,2, … , ??}in exchange for a payment. Player ??’s valuation of the object is????, and??1> ??2> ? > ????> 0. The mechanism used to assign the object is a (sealed-bid) auction: the players simultaneously submit bids (nonnegative numbers), and the object is given to the player with the lowest index among those who submit the highest bid, in exchange for a payment. In a first price auction the payment that the winner makes is the price that he bids.
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Formulate a first price auction as a strategic game and analyze its Nash equilibria. In particular, show that in all equilibria player 1 obtains the object.
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In a second price auction the payment that the winner makes is the highest bid among those submitted by the players who do not win (so that if only one player submits the highest bid then the price paid is the second highest bid). Show that in a second price auction the bid ????of any player??is a weakly dominant action: player??’s payoff when he bids????is at least as high as his payoff when he submits any other bid, regardless of the actions of the other players. Show that nevertheless there are (“inefficient”) equilibria in which the winner is not player 1.
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