Consider the following second-price (or Vickrey) auction. An object is auctioned off to two bidders. Bidder i's valuation of the object in monetary terms is vi > 0. The auction rules are that each bidder submits a bid (a nonnegative number) in a sealed envelope. The envelopes are then opened, and the bidder who has submitted the highest bid gets the object but pays the auctioneer the amount of the second-highest bid. If more than one bidder submits the highest bid each gets the object with equal probability. Assume that the valuation of each bidder is common knowledge. Then without loss of generality, players are labelled such that v1 v2.

1. Provide the best response correspondence for each bidder.

2. Show that submitting a bid of vi by each bidder constitutes a Nash equilibrium of the game.