Auction Theory
First-price vs second-price (Vickrey) auctions — Revenue Equivalence Theorem
Auction Type
First-Price
Second-Price
Both
Number of bidders n:
5
Value distribution
Uniform [0,1]
Beta(2,2) — bell shaped
Power law — skewed high
Your Bid
Your value:
0.70
Your bid (1st price):
0.52
Simulate
Simulations:
1000
Run Simulation
Theory
Optimal 1st-price bid:
b*(v) = v·(n−1)/n [uniform prior]
Vickrey (2nd-price):
Dominant strategy: bid true value v
Revenue Equivalence:
E[revenue₁] = E[revenue₂]
Both yield: (n−1)/(n+1) × v̄