Answer in Microeconomics for Abha Ahad #178767

1. There are 3 bidders named Bidder 1, Bidder 2, and Bidder 3 with valuations equal to 30, 20 and 10 respectively in a second-price sealed-bid auction for a single object. Assume that valuations of bidders are common knowledge. Bids can be any non-negative real numbers and each bidder submits a sealed bid without knowing the bids submitted by others. The bidder who submits a bid higher than the bid submitted by the other two bidders gets the object at a price equal to the highest bid submitted by the other bidders and gets utility equal to her/his valuation minus the price paid. Other (unsuccessful) bidders don’t pay anything and each one of them gets a payoff of zero. Also assume that if more than one bidder submits the highest bid, the player with the highest valuation amongst those whose bids are the highest gets the object. Give necessary and sufficient conditions for a pure strategy profile to be Nash equilibrium in this game.

Second price auctions are intended to give buyers confidence to bid their best price without excess payment.

Each player is presumed to be aware of the equilibrium strategies of other players and no player has anything to achieve by changing their own strategy. The players will do everything to increase their profit margin as defined by the game.

The players’ execution is perfect.

The players are smart enough to work out the solution.

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