Example: House auction

1
Example House auction

• Private value 75 000
• We have 3 options
• To offer 65 000
• To offer 75 000
• To offer 85 000

2
Real-estate market

• Probability that somebody offers
• 60 000 ? 20
• 70 000 ? 30
• 80 000 ? 30
• 90 000 ? 20

3
Utility table

• UTILITY Difference between payed price and
  private value (75 000).
• If we buy the house at a price higher than the
  private value, utility is negative (loss).

4
Sealed envelope

• Utility table

Weakly Dominant Strategy
OTHER
10,000
0
0
0
ME
0
0
0
0
-10,000
-10,000
-10,000
0
5
Expected Utility Sealed envelope
2 000

• Expected Utility(65,000)
• Expected Utility(75,000)
• Expected Utility(85,000)

0
- 8 000
6
SEALED ENVELOPE VS VICKREY

• Is it true that in Vickrey auctions the best
  strategy is to bid for the private valuation?

V
7
VICKREY
V

• Utility Table

Weakly Dominant Strategy
OTHER
15,000
0
0
0
ME
15,000
5,000
0
0
15,000
5,000
-5,000
0
8
VICKREY
V

• Expected Utility(65,000)
• Expected Utility(75,000)
• Expected Utility(85,000)

3 000
4 500
3 000
9
FINAL COMPARISON
SEALED ENVELOPE
10,000
0
0
0
0
0
0
0
-10,000
-10,000
-10,000
0
Greatest expected Utility 2,000
VICKREY
V
15,000
0
0
0
15,000
5,000
0
0
15,000
5,000
-5,000
0
Greatest expected Utility 4,500