1. week 10 1 COS 444 Internet Auctions: Theory and Practice Spring 2008 Ken Steiglitz ken@cs.princeton.edu

2. week 102 Moving to asymmetric bidders Efficiency: item goes to bidder with highest value Very important in some situations! Very important in some situations! Second-price auctions remain efficient in asymmetic (IPV) case Second-price auctions remain efficient in asymmetic (IPV) case First-price auctions do not … First-price auctions do not …

3. Inefficiency in FP with asymmetric bidders

4. week 104 New setup: Myerson 81 Vector of values v Vector of values v Allocation function Q (v ) : Allocation function Q (v ) : Q i (v ) is prob. i wins item Q i (v ) is prob. i wins item Payment function P (v ) : Payment function P (v ) : P i (v ) is expected payment of i P i (v ) is expected payment of i Subsumes A rs easily (check SP, FP) Subsumes A rs easily (check SP, FP) The pair (Q, P ) is called a The pair (Q, P ) is called a Direct Mechanism Direct Mechanism

5. week 105 New setup: Myerson 81 Definition: When agents who participate in a mechanism have no incentive to lie about their values, we say the mechanism is incentive compatible. Definition: When agents who participate in a mechanism have no incentive to lie about their values, we say the mechanism is incentive compatible. The Revelation Principle: In so far as equilibrium behavior is concerned, any auction can be replaced by an incentive- compatible mechanism. The Revelation Principle: In so far as equilibrium behavior is concerned, any auction can be replaced by an incentive- compatible mechanism.

6. week 106 Revelation Principle Proof: Replace the bid-taker with a direct mechanism that computes equilibrium values for the bidders. Then a bidder can bid equilibrium simply by being truthful, and there is never an incentive to lie. Proof: Replace the bid-taker with a direct mechanism that computes equilibrium values for the bidders. Then a bidder can bid equilibrium simply by being truthful, and there is never an incentive to lie.