You operate in a duopoly in which you and a rival must simultaneously decide what price to charge for the same homogeneous product. Assume each you and your rival can choose a low price or a high price. If you each charge a low price, you each earn zero profits. If you each charge a high price, you each earn profits of $3 million. If you charge different prices, the one charging the high price loses $5 million and the one charging the low price makes $5 million.

What is the Nash equilibrium for the non-repeated version of this game?

Now suppose the game is infinitely repeated. If the interest rate is 10%, can you do better than you could in the non-repeated version of this game? If your answer is yes, provide the players strategies and any other conditions that must hold.