Question

he figure below shows the payoff matrix for two firms, Firm 1 and Firm 2, selecting an advertising budget.  For each cell, the first coordinate represents Firm 1's payoff and the second coordinate represents Firm 2's payoff. The firms must choose between a high, medium, or low budget.

Payoff Matrix		Firm 1
		High	Medium	Low
Firm 2	High	(0,0)	(5,5)	(15,10)
	Medium	(5,5)	(10,10)	(5,15)
	Low	(10,15)	(15,5)	(20,20)

Use the figure to answer the following questions. Note: you only need to submit scratch work for the mixed strategy calculations.

This game can be simplified by eliminating strategies that are strictly dominated.

Which budget will Firm 1 never select (High, Medium, or Low)?

Which budget will Firm 2 never select (High, Medium, or Low)?

There are two pure strategy Nash equilibria in this game. What are they?  Submit the answers as coordinates. For example: (High, Low) represents the strategy where Firm 1 plays 'High' and Firm 2 plays 'Low'.

Pure Strategy Nash Equilibrium 1:

Pure Strategy Nash Equilibrium 2:

This game also has a mixed strategy. What is the mixed-strategy Nash equilibrium?  Enter your answers as decimal numbers, rounding to two digits when needed.

Firm 1 will set a 'High' budget with probability:

Firm 1 will set a 'Medium' budget with probability:

Firm 1 will set a 'Low' budget with probability:

Firm 2 will set a 'High' budget with probability:

Firm 2 will set a 'Medium' budget with probability:

Firm 2 will set a 'Low' budget with probability:

Answer 1