Suppose two firms (Firm 1 and Firm 2) are competing against each other in a (duopoly) market. Suppose further that the market demand is given by the equation P = 700 - 30(q1 + q2), where P is the price of the good. q1 is the quantity sold by firm 1, and q2 is the quantity sold by firm 2. Assume that the total cost of production for firm 1 is 100q1 and 100q2, for firm 2 (meaning that the additional costs to serve one customer is $100 for each firm).
a) Assuming each firm moves simultaneously. find the Nash-Coumot Equilibrium level of output for each firm. Show all of your work.
b) Assuming each firm moves sequentially. find the Nash-Stackelberg Equilibrium level of output for each firm. Show all of your work.
Every month two competing firmd (Firm A and Firm B) must decide how to spend their advertising budgets. Assume that each firm has two choices: billboard advertising or magazine advertising. The table below shows market shares for each firm given their own advertising decision and the decision of the other firs. Market shares are listed in the order (Firm A. Firm B).
Firm B
|
| |
|
Billboard |
Magazine |
|
|
Billboard
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60. 40
|
70, 30
|
|
Firm A
|
|
|
|
Magazine
|
80. 20
|
50, 50
|
Construct the expected payoff grap is for each firm. and find the Nash Equilibrium mix of billboard and magazine advertising for each firm. Show all of your work.
The table below is from the Japanese game of Janken as presented in the Art of Strategy book. Given the differences in payoffs from a traditional rock-paper-scissors game. fully explain how the optimal strategy in Janken would differ from the traditional rock-paper-scissors game.
