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Game Theory And Competition Strategies. 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. A Simple Game. Game Theory:
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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.
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
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.
Example (continued) • Player: 1. Honda. 2. Toyota. • Strategies: 1. Build a new plant. 2. Do not build a new plant.
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).
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.
The Prisoner’s Dilemma • Prisoner’s 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.
Example (continued) • Player: 1. Ron. 2. David. • Strategies: 1. Confess. 2. Do not confess.
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).
Dominant Strategies • Dominant strategy: a strategy that is better than any other a player might choose, no matter what strategy the other player follows.
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).
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
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.
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.
