Economics: Game Theory Assignment
ECON 3311 – Fall 2012
Extra Credit Homework – Game Theory
1. What is the Nash equilibrium in the following game?
2. Does the following game have a Nash equilibrium? Does it have more than one Nash equilibrium? If so, what are they?
3. Coca-Cola and Pepsi are competing in the Brazilian soft-drink market. Each firm is deciding whether to follow an aggressive advertising strategy, in which the firm significantly increases its spending on media and billboard advertising over last year’s level, or a restrained strategy, in which the firm keeps its advertising spending equal to last year’s level. The profits associated with each strategy are as follows:
What is the Nash equilibrium in this game? Is this game an example of the prisoners’ dilemma? Why?
4. In a small country there are only two major airline firms. Each firm is deciding whether to offer a frequent flyer program. The annual profits (in millions of dollars) associated with each strategy are summarized in the following table (where the first number is the payoff to Airline A and the second to Airline B):
a) Does either player have a dominant strategy? If so, what is it?
b) Is there a Nash equilibrium in this game? If so, what is it?
c) Is this game an example of the prisoners’ dilemma? Explain.
5. Two pipeline firms are contemplating entry into a market delivering crude oil from a port to a refinery. Pipeline 1, the larger of the two firms, is contemplating its capacity strategy, which we might broadly characterize as “aggressive” and “passive.” The “aggressive” strategy involves a large increase in capacity aimed at increasing the firm’s market share, while the passive strategy involves no change in the firm’s capacity. Pipeline 2, the smaller competitor, is also pondering its capacity expansion strategy; it will also choose between an “aggressive strategy” or a “passive strategy.” The following table shows the present value of the profits associated with each
Extra Credit Homework – Game Theory
1. What is the Nash equilibrium in the following game?
2. Does the following game have a Nash equilibrium? Does it have more than one Nash equilibrium? If so, what are they?
3. Coca-Cola and Pepsi are competing in the Brazilian soft-drink market. Each firm is deciding whether to follow an aggressive advertising strategy, in which the firm significantly increases its spending on media and billboard advertising over last year’s level, or a restrained strategy, in which the firm keeps its advertising spending equal to last year’s level. The profits associated with each strategy are as follows:
What is the Nash equilibrium in this game? Is this game an example of the prisoners’ dilemma? Why?
4. In a small country there are only two major airline firms. Each firm is deciding whether to offer a frequent flyer program. The annual profits (in millions of dollars) associated with each strategy are summarized in the following table (where the first number is the payoff to Airline A and the second to Airline B):
a) Does either player have a dominant strategy? If so, what is it?
b) Is there a Nash equilibrium in this game? If so, what is it?
c) Is this game an example of the prisoners’ dilemma? Explain.
5. Two pipeline firms are contemplating entry into a market delivering crude oil from a port to a refinery. Pipeline 1, the larger of the two firms, is contemplating its capacity strategy, which we might broadly characterize as “aggressive” and “passive.” The “aggressive” strategy involves a large increase in capacity aimed at increasing the firm’s market share, while the passive strategy involves no change in the firm’s capacity. Pipeline 2, the smaller competitor, is also pondering its capacity expansion strategy; it will also choose between an “aggressive strategy” or a “passive strategy.” The following table shows the present value of the profits associated with each