ECON217 | Microeconomics in Economics - Pennsylvania State University
- Consider an auction for a single good, with two bidders, each with a private value drawn independently from the uniform distribution on [0, 100]. Let values be s1 and s2 , and bids are b1 and b2 .
(a) Under a first price, sealed bid auction, what are b1 and b2 in equilibrium? (b) What is the seller’s expected revenue in this setting? (This should be a real number) (c) Under a second price, sealed bid auction, what are b1 and b2 in equilibrium? (d) What is the seller’s expected revenue in this setting? (This should be a real number) Now suppose the seller decides to hold a first price sealed-bid auction, but bids are constrained to be taken from the set {0, 50}. If both bid 0, nobody will be awarded the object; if they both bid 50, the winner will be chosen at random (with equal probabilities). (e) Does revenue equivalence hold in this setting? Why or why not? (f) Show that it is a dominant strategy for an agent never to bid 50 unless si ≥ 50. more than their true value. (g) Therefore, what are equilibrium strategies? 1b, the unconstrained auction? (h) What is the seller’s expected revenue? Is this more or less than in 1b (i) What is the expected payoff to each type of bidder? Is there any type that prefers this (constrained) auction to an ordinary first-price auction?