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 Build a new plant

16, 16 20, 15

Do not build a new plant

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

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 Confess -5, -5 0, -10

Do not confess

-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 Build a new plant

12, 4 20, 3

Do not build a new plant

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

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

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