Please help me out thanks 5 Consider the following payoff ma

Please help me out, thanks!

5. Consider the following payoff matrix for Firm A and Firm B. Firm B is an established business and Firm A is deciding whether to enter the industry for the first time. Firm B can either act forceful or reserved (payoffs in millions of dollars) in response to Firm A a. Determine if the threat of Firm B acting forceful is credible or not -if each firm has a dominant strategy Firm B Forceful 100, 100 0, 100 Reserved 100, 50 0, 100 Enter Firm A Do Not Enter b. Consider the following payoff matrix for Firm A and Firm B. Firm A sells ski equipment and Firm B sells ski clothing (complementary goods). These two firms are choosing the location of their stores in a mall and will increase profits if they choose to locate in the same corner. There are two available spots in both the NW corner and the SW corner of the shopping mall Determine whether each firm has a dominant strategy. Work through the equilibrium mixed strategy and find the expected payoffs. Firm B NW Corner (q) 50, 30 20, 15 SW Corner (1-q) 20, 15 35, 45 NW Corner (p) Firm A SW Corner (1-p) |

Solution

Ans 5/a)

From given payoff matrix we have only 1 Pure Stategy Nash Equilibrium and that equals to (Do Not Enter,Forceful)

Hence Firm B acting forceful is credible

Firm A has no dominant stratefy available with him because for strategy forceful of Firm B the best response of firm A is Do Not Enter then for every other response of firm B there will be only dominant strategy to be played by firm A but when Firm B is reserved then FIrm A will choose to Enter.

Theredore Firm A has no dominant strategy

Whereas with the similar logic firm B has weakly dominant strategy Forceful

Ans 5/b)

We have 2 PSNE here (NW Corner,NW Corner);(SW Corner,SW Corner)

Probability is already provided

we need to find the value of \"p\" for which firm A is indifferent between both of his strategies

E(NW Corner) for A=E(SW Corner) for A

50q+20(1-q)=20q+35(1-q)

30q=15(1-q)

45q15

q=1/3

Similalrly we can find for p we get

30p+15(1-p)=15p+45(1-p)

15p=30(1-p)

p=2/3

Hence Mixed Strategy NAsh Equilibrium (1/3,2/3( and (2/3,1/3) for Firm A and Firm B respectively

Expected Value for NW Corner/ SW Corner for Firm A=50(1/3)+20(2/3)=30

Expected Value for NW Corner/ SW Corner for Firm B=30(2/3)+15(1/3)=25