Assignment 2 -- Three Exercises in Best Response

You may discuss this assignment with classmates, but all your written work and code must be your own. Reference all sources. Please hand in hard copy.

1. Suppose that you are bidding in a first-price sealed-bid auction with a total of n bidders, and that values are drawn from a distribution iid (independently and identically distributed) and uniform on [0,1]. You are bidder 1. What is your best response bidding strategy b(v₁) if your competitors bid truthfully?

2. Same setup and questions as in Problem 1, except this is a second-price sealed-bid auction (a Vickrey auction), and your competitors bid the equilibrium for a first-price auction.

3. Same setup and questions as in Problem 1, except that in this auction the high bidder wins and pays the average of all the other bids (as in the class experiments), and your competitors bid truthfully.