How can strategic price and game theory can be solved. And please provide explanation how it used
Exercise 9: Strategic Pricing & Game Theory Name: Problem 9.1. The table below shows total profits earned by the auction houses Southeby's and Christie's. The profits earned by each firm is a function of both firm's own commission and also the commission of it's competitor. Christie's profits are listed first in each cell. Southeby's Strategy High Commission Low Commission Christie's Strategy High Commission $6m, $6m $8m, $2m Low Commission $2m, $8m $4m, $4m (a) If Christie's charges a low commission and Southeby's a high one, what are Southeby's profits? (b) If the two want to collude to maximize total profit, what strategies are chosen by each firm? (c) Does Southeby's have a dominant strategy in this game? yes no If so, what is it ? (d) What is the Nash equilibrium of the game? (e) At the Nash equilibrium what are profits by each firm? |$ and | $ Problem 9.2. The table below shows total profits earned by two OPEC members Saudi Arabia and Kuwait. The production allocation set by the cartel (based on population) is 10,000 barrels per day for Saudi Arabia and 3,000 barrels per day for Kuwait. Profits earned by each country is a function of both production and the world price, which decreases with totaloutput. quantity produced and the world price, which per the law of demand decreases with output. Saudi Arabia's profits are listed first in each cell. Kuwait Strategy (Barrels/Day) Low Q (2,000) High Q (4,000) Saudi Strategy Low Q (10,000) $1,000k, $200k $750k, $300k High Q (12,000) $900k, $150k $600k, $200k (a) Does Saudi Arabia have a dominant strategy in this game? yes no If so, what is it? (b) Does Kuwait have a dominant strategy in this game? yes no If so, what is it? (c) Does this game have a single Nash equilibrium? |yes no If so, what is it ? (d) How much would Saudi Arabia be willing to pay for Kuwait to stick to the cartel limit? (e) How much would Kuwait need to be compensated to stick to the cartel limit?Exercise 9: Strategic Pricing & Game Theory Name: Problem 9.3. Three manufacturers produce a drug to treat a parasite in dogs. Veterinary Medicine (b) At the competitive market price, consumer sur- ($/pill) plus is $ 20 (c) Suppose the three firms form a cartel and agree 18 to a production limit. What price will the firms 16 set? $ How many units will each firm 14 produce? Label the graph with the 12 cartel quantity QM. 10 (d) At the cartel price price, consumer surplus is $ Supply (e) Suppose one firm produces 2 thousand more than the agreed amount. The cheating firm's revenue increases decreases by Demand 10 12 14 16 18 20 Q (f) If one firm produces 2 thousand more pills than (the. pills/month) agreed, revenue for the other 2 firms increases decreases by (a) When the market is competitive, price will be $ and pills will be sold (g) Shade the area of the graph representing the each month. Label the graph with the competi- change in revenue for the cheating firm and the tive quantity QC. remaining firms
