Consider two firms that must choose whether to charge a High or a Low price for a standard product. If they both set a high price, each receives profits (in $1000) of $64 per year. If one sets a low price while the other sets a high price, the low-price firm earns profits of $72 per year while the high-price firm earns $20. If they both set a low price, each receives profits of $57.

Suppose the firms play this game repeatedly year after year, neither expecting any change to end their interaction. If the world were to end after 4 years, without either having anticipated this event, what would each firm's total profits (not discounted) be at the end of the game? How does your answer depend upon the value ofr?