use bertrand model : three brands and let's call it 1, 2, 3

supply products to same market whose demand curve Q = 100 - P

each brand i set price Pi - simultaenously indpendently of one another

Pi must be an integer multiple of 1 cent (can't be negative : example: $0 , $0.01 , $0.02 ...)

consumer buys the brands with lowest price - if lowest price is set by two or more brands, brands will share the market equally

brand1 - marginal cost $10

brand2 - marginal cost $20

brand3 - marginal cost $30

1) (P1, P2, P3) = (25,20,15)

• is it best response (yes or no for p1,p2,p3)
• is this a nash equilibrium?

2) (P1,P2,P3) = (11,12,13)

• firm1's best response should be set p1 according to other brand prices :
• is this nash equilbirium?

3) (P1,P2,P3) = (11.99, 12, 30)

• is this a nash equilibrium?
• one brand is using weakly dominated and this brand is ______ and its strategy is weakly dominated by the alternative straetgy _____________.

4) (P1, P2, P3) = (19.99 , 30, 20)

• is this nash equilibrium?
• one brand is using weakly dominated and this brand is ______ and its strategy is weakly dominated by the alternative straetgy _____________.

5) Is there any nash equilibrium in which consumers would buy product from brand 3?

yes (if yes, give numbers) or no and why

6) Is there any nash equilibrium in which consumers would pay more than 20?

yes (if yes, give numbers) or no and why