Section 20: The Many Model Thinker: Diversity and Prediction
Notes:
Ascending Price: Individuals call out bids until no one will bid a higher price.
Outcome: highest value bidder gets it at the second highest value
Second Price: Each person submits a bid. Highest bidder gets it at the second highest bid.
Outcome: Highest value bidder gets it at the second highest value.
Sealed Bid: Each person submits a bid. Highest bidder gets it at the highest bid.
Outcome: Higher you bid, the more likely you are to win.
V = Value
B = Bid
(V - B) = surplus
B = Probability of Winning
Winnings = B(V-B)
Expected winnings = B(V-B) = BV - B2
Set Derivative = 0 to get a maximum
V - 2B = 0
Optimal Bid: B = V/2
Revenue Equivalence Theorem
With rational bidders a wide class of auction mechanisms including - sealed bid, - second price,- ascending bid
produce identical expected outcomes. Roger Myerson “Optimal Auction Design” Mathematics of Operations
Research 1981
Pivot Mechanism: Idea: Pay the minimal amount you’d have to contribute for the project to be viable.
Clarke-Groves-Vickery Pivot Mechanism: Incentive Compatible: Each person has an incentive to reveal her true value.
Efficient, Always Join, Incentive Compatible, Balanced
2013-12-14 (60min) Coursera open course: Model Thinking by Scott E. Page Start from 10.07.2013, will end on 12.16.2013 Link: https://class.coursera.org/modelthinking-005/lecture/index;
Section 20: The Many Model Thinker: Diversity and Prediction
Notes: Ascending Price: Individuals call out bids until no one will bid a higher price. Outcome: highest value bidder gets it at the second highest value Second Price: Each person submits a bid. Highest bidder gets it at the second highest bid. Outcome: Highest value bidder gets it at the second highest value. Sealed Bid: Each person submits a bid. Highest bidder gets it at the highest bid.
Outcome: Higher you bid, the more likely you are to win. V = Value B = Bid (V - B) = surplus B = Probability of Winning Winnings = B(V-B) Expected winnings = B(V-B) = BV - B2 Set Derivative = 0 to get a maximum V - 2B = 0 Optimal Bid: B = V/2
Revenue Equivalence Theorem With rational bidders a wide class of auction mechanisms including - sealed bid, - second price,- ascending bid produce identical expected outcomes. Roger Myerson “Optimal Auction Design” Mathematics of Operations Research 1981 Pivot Mechanism: Idea: Pay the minimal amount you’d have to contribute for the project to be viable. Clarke-Groves-Vickery Pivot Mechanism: Incentive Compatible: Each person has an incentive to reveal her true value. Efficient, Always Join, Incentive Compatible, Balanced