Question

There can be more than one Nash Equilibrium or no Nash Equilibrium at all. In the following game HA and CA are trying to decide which segment of the market to appeal to with advertising, prices,special promotions, etc. Each firm has two strategies available: appeal high income customers, or appeal to lower income customers.

^If both try to appeal to high income customers they will directly compete against each other and each firm gets a payoff of 50.

^If both try to appeal to lower income customers they will, again, directly compete against each other and each firm gets a payoff of 50.

^If HA appeals to high income customers, and CA appeals to lower income customers, then each firm gets a payoff of 80.

^If CA appeals to high income customers, and HA appeals to lower income customers, then each firm gets a payoff of 70.

Does this firm have more than one Nash Equilibrium or no Nash Equilibrium? If it has more than one, what are the equilibria?

Answer 1

Payoff matrix

HA/CA	High	low
High	(50,50)	(80*,80•)
Low	(70*,70•)	(50,50)

NE pure strategy :

(HA appeals to low income, CA appeals to high income )

(HA appeals to high income, CA appeals to low income )

​​​​​​More than one NE