The Companies Childlife And Backyard Produce And Sell Wooden Swing Sets For Children. Each Company Can Set Either A High Or A Low Price For A Standard Two-Swing, One-Slide Set. If They Both Set A High Price, Each Receives Profits Of 100 Thousand Dollars Per Year. If One Sets A Low Price While The Other Sets A High Price, The Low Price Firm Earns Profits

2. The companies Childlife and Backyard produce and sell wooden swing sets for children. Each company can set either a high or a low price for a standard two-swing, one-slide set. If they both set a high price, each receives profits of 100 thousand dollars per year. If one sets a low price while the other sets a high price, the low price firm earns profits of 150 thousand dollars per year while the high price firm earns 20 thousand dollars per year. If they both set a low price, each receives profits of 80 thousand dollars per year. (a) What are the Nash equilibrium strategies and payoffs in this simultaneous- move game if the players make price decisions only once? What kind of game is it? (b) If the two firms play this game for a fixed number of periods, say for four years, what would each firm's total profits be at the end of the game if the interest rate is zero? Explain how you arrived at your answer. (c) Suppose that the two firms play this game repeatedly forever. i. Can an outcome in which both firms set a low price in every period be sustained as a Nash equilibrium? Explain your answer. ii. Can an outcome in which both firms set a high price in every period be sustained as a Nash equilibrium if the interest rate is r = 0.1? If yes, what strategies could be used to sustain this outcome as a Nash equilibrium? iii. Can an outcome in which both firms set a high price in every period be sustained as a Nash equilibrium if the interest rate is T= 0.5? Explain you answer.