game value: the expected payoff when both players play thei

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2 Fair Game
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Key Terms

• Game Value the expected payoff when both players
  play their maximin/minimax strategies
• Fair Game a game for which the Game Value 0

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Game Matrix
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Part A Calculate Game Value

• Step 1 Calculate maximin strategy for Dave
• EP Andy 1,0 1(1-p)(5) 1(p)(2) 5 5p 2p
  5-3p
• EP Andy 0,1 1(1-p)(-3) 1(p)(4) -3 3p
  4p -37p
• 5-3p -37p
• 10p 8
• p .8, 1-p .2 ? Daves maximin strategy .2,
  .8

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Part A Calculate Game Value

• Step 2 Calculate minimax strategy for Andy
• EP Dave 1,0 1(1-q)(5) 1(q)(-3) 5 5q
  3q 5-8q
• EP Dave 0,1 1(1-q)(2) 1(q)(4) 2 2q 4q
  22q
• 5-8q 22q
• 10q 3
• q .3, 1-q .7 ? Andys minimax strategy .7,
  .3

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Part A Calculate Game Value

• Step 3 Use Strategies to find Game Value
• Four possible outcomes
• 1. Both choose Option 1
• EP (.2) x (.7) x (5) .14 (5) .7
• 2. Dave picks Option 2, Andy picks Option 1
• (.8) x (.7) x (2) .56 (2) 1.12
• 3. Dave picks Option 1, Andy picks Option 2
• (.2) x (.3) x (-3) .06 (-3) -.18
• 4. Both choose Option 2
• (.8) x (.3) x (4) .24(4) .96
• Sum Game Value
• .7 1.12 -.18 .96 2.6 Game Value

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Part B Examples of Fair/Unfair Games

• Fair
• Vegas Roshambo
• The Finger Game
• Unfair
• Game in Part A
• Ninja-Pirate Air War
• The Worst Case (Unit 1, Set B)

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Part C Fair Game Matrices