Book contents
- Frontmatter
- Contents
- Preface
- 1 Theory 1: Introduction
- 2 Theory 2: Simultaneous Games
- 3 Example: Selecting a Class
- 4 Example: Doctor Location Games
- 5 Example: Restaurant Location Games
- 6 Using Excel
- 7 Example: Election I
- 8 Theory 3: Sequential Games I: Perfect Information and no Randomness
- 9 Example: Dividing A Few Items I
- 10 Example: Shubik Auction I
- 11 Example: Sequential Doctor and Restaurant Location
- 12 Theory 4: Probability
- 13 France 1654
- 14 Example: DMA Soccer I
- 15 Example: Dividing A Few Items II
- 16 Theory 5: Sequential Games with Randomness
- 17 Example: Sequential Quiz Show I
- 18 Las Vegas 1962
- 19 Example: Mini Blackjack and Card Counting
- 20 Example: Duel
- 21 Santa Monica in the 50s
- 22 Theory 6: Extensive Form of General Games
- 23 Example: Shubik Auction II
- 24 Theory 7: Normal Form and Strategies
- 25 Example: VNM POKER and KUHN POKER
- 26 Example: Waiting for Mr. Perfect
- 27 Theory 8: Mixed Strategies
- 28 Princeton in 1950
- 29 Example: Airport Shuttle
- 30 Example: Election II
- 31 Example: VNM POKER(2, r, m, n)
- 32 Theory 9: Behavioral Strategies
- 33 Example: Multiple-Round Chicken
- 34 Example: DMA Soccer II
- 35 Example: Sequential Quiz Show II
- 36 Example: VNM POKER(4, 4, 3, 5)
- 37 Example: KUHN POKER(3, 4, 2, 3)
- 38 Example: End-of-Semester Poker Tournament
- 39 Stockholm 1994
- Bibliography
- Index
15 - Example: Dividing A Few Items II
- Frontmatter
- Contents
- Preface
- 1 Theory 1: Introduction
- 2 Theory 2: Simultaneous Games
- 3 Example: Selecting a Class
- 4 Example: Doctor Location Games
- 5 Example: Restaurant Location Games
- 6 Using Excel
- 7 Example: Election I
- 8 Theory 3: Sequential Games I: Perfect Information and no Randomness
- 9 Example: Dividing A Few Items I
- 10 Example: Shubik Auction I
- 11 Example: Sequential Doctor and Restaurant Location
- 12 Theory 4: Probability
- 13 France 1654
- 14 Example: DMA Soccer I
- 15 Example: Dividing A Few Items II
- 16 Theory 5: Sequential Games with Randomness
- 17 Example: Sequential Quiz Show I
- 18 Las Vegas 1962
- 19 Example: Mini Blackjack and Card Counting
- 20 Example: Duel
- 21 Santa Monica in the 50s
- 22 Theory 6: Extensive Form of General Games
- 23 Example: Shubik Auction II
- 24 Theory 7: Normal Form and Strategies
- 25 Example: VNM POKER and KUHN POKER
- 26 Example: Waiting for Mr. Perfect
- 27 Theory 8: Mixed Strategies
- 28 Princeton in 1950
- 29 Example: Airport Shuttle
- 30 Example: Election II
- 31 Example: VNM POKER(2, r, m, n)
- 32 Theory 9: Behavioral Strategies
- 33 Example: Multiple-Round Chicken
- 34 Example: DMA Soccer II
- 35 Example: Sequential Quiz Show II
- 36 Example: VNM POKER(4, 4, 3, 5)
- 37 Example: KUHN POKER(3, 4, 2, 3)
- 38 Example: End-of-Semester Poker Tournament
- 39 Stockholm 1994
- Bibliography
- Index
Summary
A glimpse into statistics, mechanism design, and incomplete information
Prerequisites: Chapters 1, 8, 12, and 9.
You have two lovely daughters, Ann and Beth. A friend gave you a few presents for them. You don't know how much the presents mean to your daughters, but you want to be fair, and you want them to be as happy as possible. How would you distribute them?
We don't have a game yet, only the description of a problem.
The most important assumption, used in Section 15.4, is that the daughters are so close to each other that they can estimate the value of each item to their sister. The more complicated incomplete information situation where this is not the case is briefly discussed in Section 15.5.
You could distribute the items yourself. Since you don't know about the values of the items to your daughters, it may seem fairest to give about the same number of items to each. However, the outcome is not fair if one daughter is much happier with your choice than the other. Another disadvantage of the method is that it is not efficient—the items are distributed without considering their values to Ann and Beth. Since you don't know these values, but Ann and Beth do, they should be involved in the distribution process. This will make it more likely that they get items that are valuable to them.
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- Information
- Game Theory Through Examples , pp. 110 - 120Publisher: Mathematical Association of AmericaPrint publication year: 2014