4. (20 points) In class we looked at a patent race modeled as a rent-seeking game. In actual patent races, it might be that rent-seeking expenditures by the losers in the race nonetheless lower the value of the prize to the winner, by allowing the losers to \"invent around the patent\". Let's add that feature to the class model. Specically, Firm A and Firm B are once again 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 minus the expenditures of the other rm. 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. As in the stande rent-seeking game, the probability that rm A will win is given by Pa = Xa/(Xa + Xb), so the probability that rm B will win is Xb/(Xa + Xb). Given that both competitors are expected prot maximizers, nd a symmetric Nash equilibrium for Xa and Xb in this patent race game with an eroding prize. How much of the original $100 prize is \"dissipated\" by the overall to secure the patent, along with the equilibrium amount of ' ' of the prize