Assume that Apple and Samsung are considering the development of an innovative battery for smartphones that lasts for 6 months and based on a newly discovered chemical element called Gulium. Each ton of Gulium costs K, while the venture has 70% probability of success and requires 4 tons. Construct the payoff matrix with the 3 potential outcomes (neither firm buys the Gulium, only one firm buys it and the other does not, both firms buy it), and explain how the Nash equilibrium is related to the cost of each ton of Gulium, K. [Use the notation ΠΠMM and ΠΠDD for the monopoly and duopoly profits, respectively.]