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
7 - Example: Election 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, 2, and 6.
The president of the USA is elected by electors from all 50 states. All the electoral votes from a state go to the most popular candidate in that state. If one week before the election a candidate knows that she is behind in a few states, and leading in others, what would be a good strategy for the remaining time? Concentrating on those states where she is behind, or accepting that they are lost and concentrating on others? The decision will depend on several factors, including whether the state can still be turned, and on the size of the state. California is more important than Montana in the presidential election. In this chapter we look at a simplified model with only three districts and analyze a few cases formally. Looking at simpler cases may allow us to extract rules for larger situations.
First Example
We start with a special game, part of a family of games that will be introduced later.
ELECTION 1 or ELECTION(7, 8, 13| −1, −1, 1|3, 3) In Kalumba there are three electoral districts, C, D, and E. As in the election of the President of the USA, the President of Kalumba is elected by electoral votes. There are 7 electoral votes from district C, 8 from district D, and 13 from district E. Districts do not split electoral votes. There are two presidential candidates, Ann and Beth, and in the last phases of their campaigns they simultaneously decide how to allocate the three remaining resources each has. Each must be allocated entirely to one district. A district may receive more than one resource. Each district will vote for the candidate who put more resources into the district (not just during the last phase), and will abstain in case of a tie. In districts C and D, Ann is 1 resource unit behind, and in district E, Ann has an advantage of 1 resource unit. How should Ann and Beth distribute their resources?
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- Information
- Game Theory Through Examples , pp. 47 - 52Publisher: Mathematical Association of AmericaPrint publication year: 2014