4. (16 points) Firm A and Firm B are in a race to secure a patent. The winner of the race (the rst to develop the new invention) will receive the patent, which will be worth $100. Let Xa represent the amount of money that rm A spends on the race, and let Xb represent the amount of money that rm B spends on the race. Imagine that the probability that rm A will win is given by Pa = 2Xal(2Xa + Xb), so the probability that rm B will win is Xb/(ZXa + Xb). Find a Nash equilibrium for Xa and Xb in this biased patent race game, where rm A's expenditures are twice as potent as rm B's. Is total expenditure (Xa + Xb) higher, lower, or the same as when the two rms engage in an unbiased patent race