Game Theory And Competition Strategies

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Game Theory And Competition Strategies
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Chapter Preview

• Analyze simple game in order to understand the
  concept of a Nash Equilibrium.
• Learn about dominant VS dominated strategies and
  pure versus mixed strategies.
• Learn how to find Nash Equilibrium.

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A Simple Game

• Game Theory
• Concern with the analysis of optimal decision
  making in competitive situations.
• Strategy
• A plan for the action that a player in a game
  will take under.
• There are
• - players
• - strategies
• - outcomes

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The Nash Equilibrium

• Nash Equilibrium
• a situation in which each player in a game
  chooses the strategy that yields the highest
  payoff, given strategies chosen by the other
  players.

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Example
Toyota
Build a new plant Do not build a new plant
Honda Build a new plant 16, 16 20, 15
Do not build a new plant 15, 20 18, 18
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Example (continued)

• Player
• 1. Honda.
• 2. Toyota.
• Strategies
• 1. Build a new plant.
• 2. Do not build a new plant.

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Example (continued)

• Outcome
• 1. Honda build a new plant and Toyota build
• a new plant 16 for Honda, and 16 for
• Toyota (16, 16).
• 2. Honda build a new plant and Toyota do
• not build a new plant 20 for Honda, and
  
• 15 for Toyota (20, 15).

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Example (continued)

• Outcome
• 3. Honda do not build a new plant and Toyota
  build
• a new plant 15 for Honda, and 20 for
• Toyota (15, 20).
• 4. Honda do not build a new plant and Toyota
  do
• not build a new plant 18 for Honda, and
  
• 18 for Toyota (18, 18).
• Nash Equilibrium for each firm the strategy
  build a new
• plant was better
  than do not build,
• no matter what
  strategy the other firm chose.

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The Prisoners Dilemma

• Prisoners dilemma
• a game situation in which there is a tension
  between the collective interest of all of the
  players and the self interest of individual
  players.

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Example
David
Confess Do not confess
Ron Confess -5, -5 0, -10
Do not confess -10, 0 -1, -1
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Example (continued)

• Player
• 1. Ron.
• 2. David.
• Strategies
• 1. Confess.
• 2. Do not confess.

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Example (continued)

• Outcome
• 1. Ron confess, and David confess, -5 for
• Ron and -5 for David (-5, -5).
• 2. Ron confess, and David not confess, 0 for
  
• Ron and -10 for David (0, -10).
• 3. Ron not confess, and David confess, -10
  for Ron
• and 0 for David (-10, 0).
• 4. Ron not confess, and David not confess,
  -1 for
• Ron and -1 for David (-1, -1).

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Dominant Strategies

• Dominant strategy
• a strategy that is better than any other a
  player might choose, no matter what strategy the
  other player follows.

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Example
Ambassador
Build a new plant Do not build a new plant
Marutti Build a new plant 12, 4 20, 3
Do not build a new plant 15, 6 18, 5
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Example (continued)

• Outcome
• 1. Marutti build a new plant and Ambassador
  
• build a new plant 12 for Marutti, and 4
  for
• Ambassador (12, 4).
• 2. Marutti build a new plant and Ambassador
• do not build a new plant 20 for
  Marutti,
• and 3 for Ambassador (20, 3).

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Example (continued)

• Outcome
• 3. Marutti do not build a new plant and
  Ambassador
• build a new plant 15 for Marutti, and 6
  for
• Ambassador (15, 6).
• 4. Marutti do build a new plant and
  Ambassador
• do not build a new plant 18 for
  Marutti,
• and 5 for Ambassador (18, 5).
• Note
• - Marutti does not have a dominant strategy.
• - Nash equilibrium Ambassador builds a new
  plant, and Marutti does not

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Example (continued)

• Note
• - Marutti does not have a dominant strategy.
• - Nash equilibrium Ambassador builds a new
• plant, and Marutti does not.
• - Ambassador has dominant strategy.

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Dominated Strategies

• Dominated Strategies
• a strategy such that the player has another
  strategy that gives a higher payoff no matter
  what the other player does.
• The opposite of a dominant strategy.

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Example

Build Large Build Small Do Not Build
Build Large 0, 0 12, 8 18, 9
Honda Build Small 8, 12 16, 16 20, 15
Do Not Build 9, 18 15, 20 18, 18
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Case Find Nash Equilibrium?
Coke
10.50 11.50 12.50 13.50
Pepsi 6.25 66, 190 68, 199 70, 198 73, 191
7.25 79, 201 82, 211 85, 214 89, 208
8.25 82, 212 86, 224 90, 229 95, 225
9.25 75, 223 80, 237 85, 244 91, 245