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: 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: Toyota Build a new plant Do not build a new plant Honda 16, 16 20, 15 15, 20 18, 18

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 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 David Confess Do not confess Ron -5, -5 0, -10 -10, 0 -1, -1

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

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.

Example Build Large Build Small Do Not Build 0, 0 12, 8 18, 9 Honda 8, 12 16, 16 20, 15 9, 18 15, 20 18, 18

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