Consider a two-player game between Child’s Play and Kid’s Korner, each of which produces and sells wooden swing sets for children

Consider a two-player game between Child’s Play and Kid’s Korner, each of which produces and sells wooden swing sets for children. Each player can set either a high or a low price. If they both set a high price, each receives profits of $64,000 per year. If one sets a low price and the other sets a high price, the low-price firm earns profits of $72,000 per year, while the high-price firm earns $20,000. If they both set a low price, each receives profits of $57,000.

(a) If the two firms decide to play this game for a fixed number of periods—say, for 4 years—what would each firm’s total profits be at the end of the game (without discounting)?

(b) Suppose the two firms play this game repeatedly forever. Let each of them use a grim strategy in which they both price high unless one of them “defects,” in which case they price low for the rest of the game. If r is the rate of return, cooperation between the two firms can be sustained for all r less than _______ (please enter an exact answer).

(c) Suppose the two firms play this game repeatedly forever. Let each of them use a grim strategy in which they both price high unless one of them “defects,” in which case they price low for the rest of the game. Suppose now that the firms know that there is a 10% probability that one of them may go bankrupt in any given year. If bankruptcy occurs, the repeated game between the two firms ends. Under these circumstances, cooperation can be sustained for all r less than _______ (please enter an exact answer).

(d) Suppose the two firms play this game repeatedly forever. Let each of them use a grim strategy in which they both price high unless one of them “defects,” in which case they price low for the rest of the game. Suppose r is 0.5 (r=50%). Suppose p is the probability with which the game continues after any given year. Cooperation can be sustained for all p greater than _______.