👨‍🏫 Notes on Lecture 8b

Pindyck and Rubinfeld: Sections 13.1 - 13.4

See also: 👨‍🏫L8a Mon. Comp. and Oligopoly (April 7)

Game Theory

Ways to solve a game

1. Nash equilibrium
2. Dominant strategies

Notes:

• “Row” means the player who chooses the row strategy.
• First payoff is generally for Row Player. Second payoff is for Column player.

To add rectangles for ROW

1. Choose one action for column and put a “blue circle” around that column.
2. Underline the payoffs for Row in that circle
3. Put a rectangle around the higher underlined #
4. Do the same for the other column.

Intuition: The blue circle says that Row believes Column will confess. (It represents Row’s beliefs about his opponent.) Row cares only about his payoffs - these are indicated by the underlines. He chooses the higher payoff, so the rectangle indicates that row’s choice is optimal in that cell.

Nash Equilibrium:
Two rectangles in same cell = Nash = optimal for both players

Dominant Strategy:
A full row of rectangles for Bruce means that Confess is always optimal, so it is a dominant strategy for the row player.
A full column of rectangles for Rob means that confess is always optimal, so it is a dominant strategy for Rob.