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
9 - Example: Dividing A Few Items I
- 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
Prerequisites: Chapters 1 (and maybe 8).
A few items, five or six, are distributed to Ann and Beth by letting them choose one by one. If they alternate choosing, beginning with Ann, we call the games ABABA and ABABAB, depending on the number of items. For different choice orders we get different games. For instance, ABBABA is a game with six items where Ann chooses one item, Beth chooses two, Ann chooses one, Beth one, and Ann takes the remaining one. In the same way the games ABBAAB could be defined for six items, and the games ABBAB, ABBAA, and ABABB for five items.
We assume that the items may have different values to Ann and Beth, that the players know how they both value each item, and that the game's total value to a player is the sum of the values of the items she got. Both players want to get as much value as possible.
Let us label the items as item C, D, … and let a(C) and b(C) denote the values of item C for Ann and Beth, and so on.
Greedy Strategy
Isn't the way how to play these games obvious? Wouldn't each player choose the most valuable remaining item(s) whenever she has to choose? Let's call this strategy the greedy one. Instant gratification now!
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- Chapter
- Information
- Game Theory Through Examples , pp. 70 - 76Publisher: Mathematical Association of AmericaPrint publication year: 2014